There are massive amounts of difference between different Muslims - 1.3 billion of them on the planet. I'm somewhat familiar with Arab culture and Islam (the two are not the same) due to my ex as mentioned previously. I also lived in the Gulf for several years and can speak a little Arabic and read and write the script. Bearing in mind there are massive cultural differences between different Arabs, e.g. Gulf, Levantine, North African etc (for just the very broad differences). Plus individual differences - just because someone's from a Muslim family doesn't mean they're a practising Muslim or even any kind of Muslim. Also bear in mind that there are Arab Christians and other religions as well.
If you want to know the specific details of day to day Islamic practices like the 5 daily prayers, I'd recommend getting a guide for new converts to Islam. There's the Teach Yourself Islam book by Ruqaiyah Waris Maqsood (apologies if I transliterated her name wrong, there is about 100 different ways to spell Ruqayya in English and only one in Arabic) which is a good Islam 101 guide that's appropriate for new Muslims and non-Muslims who want to educate themselves about Islam. It's also good for differentiating between the actual religious teachings of Islam and cultural practices of various different Muslims. It will help massively with researching Islam for fiction, but you also need to research the character's culture separately as the two are not the same thing.
Friday prayers (done just after noon on a Friday) are obligatory for all men who are able bodied enough to get there, but optional for women. A few masjids take the whole "optional for women" thing to mean they don't need to provide any facilities for women at all. Even when there are prayer rooms for women, they're usually smaller than the men's prayer room. There is nothing to prevent a large prayer room being divided in half, the men will pray in front and the women at the back and some masjids will do this.
Before praying you have to wash (wudu) in a very specific way that includes (amongst other things) washing the feet. If Muslims are praying somewhere where there's a multifaith prayer room e.g. at a university, then the lack of feet washing facilities can cause issues with both Muslims and non-muslims (e.g. people washing their feet in the sink in a conventional western bathroom). for full details of how to do wudu (if needed) see the above-mentioned book. You don't wear shoes in a masjid. In the women's prayer room women don't have to wear headscarves as there are no men around. If it's a prayer room with with both men and women in it, then women will wear headscarves. Also, there's more to hijab (modesty) than wearing a headscarf (see the above-mentioned book). And hijab applies to men as well.
Children before the age of puberty are considered innocent and that they should see the masjid as a fun place, so kids running amuck while prayers are going on is normal. Arabs are particularly fond of children. Some imams will try to involve the children in praying but this isn't forced. Some masjids may do classes for children, but the content and the way its taught varies massively. Classes and social gatherings for adults, events for fundraising, events for charity, special days for teaching the local non-Muslims that they're not terrorists and are actually quite a friendly bunch they can come and have a cup of tea with, all can be happening there. Also, religious events such as marriages will take place there from time to time, people converting to Islam, and funeral prayers - see the above-mentioned book for the specific details. If people just so happen to be in the masjid when funeral prayers are going on, they're expected to attend as it's supposed to be the whole community and if you pray at the same masjid you're part of the community whether you know the person who died or not.
A well-run masjid has a very community feel and people are always welcome. There's no time when you can't go (although there are times when you're not supposed to pray - see the book I've referred to multiple times already - but you can go and sit in the masjid at those times) albeit you might end up randomly getting involved with something going on. For example if they need someone to witness someone converting to Islam, they tend to just grab random people. It will be much, much quieter when it's not Friday and there will only be the super-dedicated in the masjid for fajr prayers (done between dawn and first light). During Ramadan, more people go to the masjid to pray and masjids will provide food at maghreb (sunset) time after the maghreb prayers, for people to break their fast. Typical fare is lamb curry with rice. People donate food and bring in food they've prepared, or it might be donated by a local Muslim-owned restaurant (hence the predominance of curry, at least in the UK!). Eid prayers are like Friday prayers but done earlier in the day on Eid, and you thought the masjid was busy on a Friday, you haven't seen busy until you've seen Eid prayers. Muslims pray the standard 5 prayers a day plus optional extra ones, if they don't pray at the masjid they pray at home (or work, or wherever they happen to be*)
*if you're on an aeroplane, finding out which way Mecca is while you're mid flight can be a challenge but we always flew Qatar Airways and the cabin crew could always help with pointing my ex in the right direction (literally) because it's a common query - when travelling you only do 3 prayers a day but if you're flying across several time zones you may still have to do one of those three prayers on the plane. Oh and a literary reference: I **love** the way Jazz's dad in Artemis by Andy Weir handled the whole "which way is Mecca?" thing while living on the moon.
The only times I've heard of masjids not being open all the time is when there's a risk of vandalism and racist attacks from the local non-Muslim communities, which is heartbreaking. Non-Muslims often don't realise the full impact such things have on communities.
Hope some of that info's helpful - just to reiterate again, there is so much variation with Muslims that it's hard to give info without some people coming along and saying it's not like that in their local masjid or whatever. Also, in Arabic, big masjids are called jama'a but British Muslims just tend to call them all masjids, or mosque when speaking to non-Muslims. Dunno how it works in the USA if I'm honest. Also, the Arabic terms mentioned above may be called something completely different by Urdu speakers and speakers of other languages. I know the names of all the prayers in Arabic, but can barely understand the same words when spoken by Urdu speakers, plus other languages having their own terms for things. Muslims are culturally and linguistially extremely diverse.
Feel free to ask any more questions if you want.
It's probably because my experience is strongly biased towards Arabic and Arabic speakers, on account of my ex and living in the Gulf. British Muslims are more often Pakistani and as far as I can remember, they call it a masjid. But it's very interesting to learn about all the regional differences. People - myself included - forget just how huge and diverse the Muslim population is.