Scenario a...batter sacrifices himself by bunting,a runner on third comes home ,the batter has earned himself an RBI...Run Batted In.
Scenario b..If the bases are empty and a batter hits a home run he scores one run as he runs all the way round the diamond.Depending on how many bases have runners the batter hitting the home run will score 1,2,3,or 4 runs as all the runners make their way to home plate.
Scenario c..Much the same as b except the batter gets in the ball into the outfield and the runners are able to successfully make round the bases and home without getting tagged out.Note.. and infield home run is not a common occurance.
ERA is a s you say Earned Run Average and is a pitching statistic.It means the average number of runs given up by a pitcher per nine innings games.As a starting pitcher rarely pitches a entire game and obviously relief pitchers don't either the calculation is a bit complicated.Have a look at this
http://mlb.mlb.com/stats/sortable.jsp#elem=%5Bobject+Object%5D&tab_level=child&click_text=Sortable+Player+pitching&game_type='R'&season=2013&season_type=ANY&league_code='MLB'§ionType=sp&statType=pitching&page=1&ts=1372865173315
Hover your mouse over the ERA column header and itll explain it.
The lower the ERA the better the pitcher
I hope this helps.