I am new to this and I see a lot of sits that I would be very interested in but should I hold out for a better offer if the original offer hasn’t responded that leads to my second question, do they let you know if they don’t choose you or are we notified somehow that we’ve not been chosen so that we could go ahead and fill that date with another sit?
@Judydove welcome to the forum. Apply for all the sits you want to, you are not bound by anything just because you have applied. As long as you are honest about what you are doing there is no problem. Once a sit is confirmed, then it’s not appropriate to drop that one for a better one. A confirmed it is a confirmed sit. My experiences is that some people acknowledge your application and others don’t. Even if you don’t receive a message from the HO When they accept someone else, you will automatically be declined, and that message will go to your inbox. Some sitters withdraw their application if they haven’t heard from The Ho within 72 hours or so, which is the suggested response time from THS. If you’ve applied for sits with conflicting dates, the minute that you confirm one of them, you can withdraw your application for the any others. Any time you want to withdraw an application, you just untick the box in your messages that you originally ticked to apply for the sit. 
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Then the success rate of applications is often quite low. So apply to anything that you would like.
But some advice in all well-meaning: use interpunction in your applications and in your profile.