I was just wondering if you could get time signatures where the bottom number is 3,5,6,7,9,10,11 and so on. I did not know if you could have dotted notes as your base note
Yes. This kind of time signature is called Irrational.
An irrational time signature is one where the denominator isn't a power of two (like the examples you provided).
There has been another similar question here;
Where the asker provides a link from Wikipedia that has many compositions in irrational time signatures.
No, basically. But of course it depends on what you mean by "could you get?"
A time signature has a bottom number (it's not a denominator, because a time signature is not a fraction) which is a power of 2, representing one of the series of binary-divided notes from semibreve ("whole note") downwards. The top number shows how many of these note-values make up a bar (measure). It would be nice if the bottom number showed how big a beat is, but this is not true: if each beat is a dotted crotchet, then the number on the bottom "ought" to be 3/8, but instead 8 is written on the bottom, and the number on the top is the number of beats multiplied by 3. Similarly, if there are 3 beats each divided into 5 quavers, the time signature is 15/8 (e.g. Scriabin op. 11-14). (And of course this is ambiguous: it could be 5 beats of dotted crotchets.)
You asked about numbers like 3, 5, 7 etc., but unfortunately it is not clear what these would mean, because they do not obviously refer to any sensible notes: if my binary arithmetic is to be trusted, 1/3 in binary is 0.010101..., so 3 on the bottom means that each beat is represented by (let's use American here!): 1/4 + 1/16 + 1/64 + ..., and unending series of notes.
Meanwhile, those regarding fame as more important than music can write anything they like, any some people may buy it.
Carl Orff in Carmina Burana (and I guess elsewhere) pioneered a much better system in which you write the note symbol for each beat (including dotted notes) on the bottom, and the number of beats on the top, but this has never really caught on.