That's part of the reason why host nations receive an average 40% medal bump in their final tally. More teams sent = more opportunities to medal.
Nah, don't think that makes a difference. Host nation teams automatically qualify for events, so you can throw athletes at events that perhaps wouldn't qualify normally. Those guys will never medal, but it's great to get the experience of a major competition - and a home one too.
The main reason some home teams get a boost is financial. A host nation doesn't want to be embarassed so they'll invest more in sports and that reaps rewards. Team GB I think started investing even before they won the Olympic bid, so we did really well in Beijing.