Telephone and electricity, no. Neither was really available to the general public then in small towns. Electricity would become more available in the next several years, however.
Indoor plumbing -- depends on what you mean. Indoor toilet? Highly unlikely. They would have had an outhouse. Water heaters were also not in wide circulation, so water would have been COLD. (They'd been invented, but they were definitely not in wide use.)
A cold-water faucet in the kitchen, either pumped or under pressure, MIGHT have been possible, depending on the ingenuity of the homeowner. If they, for example, lived on a farm and had a water tank above the home (on a hill, or perhaps a windmill filled stock tank) gravity fed water would be possible.
I know of the remains of a 1900's era ranch house in Arizona -- all that's left is the outline of the house's walls. However, over a century later, there's still running water at the house from a pipe that comes out of the ground, because the rancher had found a spring on the hillside above the house, built a springbox, and then used gravity to feed water to the house. I don't know if there was originally water plumbed inside the house or if they just had a tap in the yard.
The period between the late 1800's and the 1930's is FULL of technological developments. If you're writing a story set 1905, plan on doing a ton of research -- you'll need to figure out if something is (a) invented and (b) if your characters would have actually used/owned/known about it.