easy questions

[devdog69]

I got conned into a few JV games this summer and had a couple of questions. I think I already know the answers but humor me.
Sitch 1: Pitch bounces off the dirt and then strikes the batter in the shin. He still gets first base right?
Sitch 2: Throw coming in from outfield rolling behind runner trying to score...catcher comes near the baseline bending to pick up ball about three feet before the plate, runner does not slide and there is contact with the catcher...after calling him safe there was a protest and after conferencing with BOTH coaches and the runners coach admitting he should have been called out I changed my call to 'out'. I told him I wanted the call to be right and he reluctantly agreed. Did I , eventually, get this right and what exactly is the rule on the runner sliding. I have been told that the runner must 'avoid contact' and if that means sliding then he must slide?