How strict are agents on absolutely perfect grammar?

I’ve had about seven rejection letters so far from various English Literary Agents, all of whom have either said that they do not see a market for my novel, or are unsure of the standard of writing. Without wishing to sound boastful, I hold several degrees in various subjects and would consider myself proficient in the use of the English language as well as being able to write in a scintillating style to keep readers interested.

However, in my manuscript, I have chosen a particular literary style which is somewhat more colloquial in expressions and turns of phrase. Furthermore, it does not always strictly obey the rules of grammar, but might be more similar to the way one might either speak or think. For example, I might start certain sentences with “And” or “But”, as in the following example (off the top of my head):

She searched everywhere for the torch. Where was it? Did it really matter if she went on without it? But she needed it. Yes. She couldn’t go on in the dark, for she could stumble over something and injure herself. And how would that help the others if she did that?

Please ignore the fact that this may not be brilliant writing in that paragraph. I simply came up with it in less than a minute in order to illustrate certain stylistic traits. What I’m really trying to analyse here is the following:

a) Do agents like sentences which are brief like that above? – I have written it in that almost staccato style in places to simulate the sudden surge of tension and rapid-fire thoughts that might go through a person’s head in a panic situation.

b) Do agents frown upon sentences which start with “And”, “But”, "Because" etc or are they discerning enough to realise that this was done as stylistic device? Or would they simply think that I am unable to construct a sentence properly? [see, I’ve done it even in this paragraph starting with “Or” for effect.]

c) Would the agents prefer it if I wrote in a very formal English style or is it acceptable to write colloquially/ conversationally?

d) What about ending sentences like: “who could she give it to?” as opposed to “to whom could she give it?” which could end up sounding rather stiff?

The problem is that the agents haven’t specified exactly which parts of my writing they do not find up to the standard required to be sent to a publisher. Should I try to change the style to a more strict, grammatical style or should I leave it as it is? And what if the short, staccato style/ starting a sentence with “And” etc is a style they like and I get rid of that, leaving the novel written in a rather dry manner? [see, here’s another example of starting with “And” again, (I could’ve started it with “but”) because it sounds more effective than having it all as one sentence].

What do people here think?

I would be grateful for your feedback.

Thank you