Question: If I played a super high stealth 5e rogue who stayed physically far from combat and in little danger but dealt out a majority of the damage in a battle....would I get full XP?
Yes for the battle; the Rogue got involved and helped out.
Had, however, said Rogue not done anything to help in the battle (e.g. all she did was keep watch outside the door) then no xp for it for her.
Second Question: Do you actually have a problem at your table with players who just don't join battles at all because they are afraid of losing a character?
At my own table, not very often lately; but it was almost chronic with one or two players in the past. At the table where I'm a player it's happened enough to be a Known Issue, though it's certainly improved of late.
I have never....in my 30+ years of gaming ever seen that happen with the rare exception of an almost dead character the rest of the party was trying to rescue. Everyone fights every battle....and we have used milestone levelling exclusively since 3e Age of Worms.
I'm talking about characters in good condition. Obviously if a character is close to death or otherwise incapable of doing much of use, that's different.
And it can be more subtle than simply staying out completely, e.g. a Fighter who somehow never ends up facing the toughest/deadliest opponent in a group of foes, as in a spoken or unspoken "You guys deal with the Giant, I've got the Orcs" type of thing. Once in a while: fine. As a pattern: annoying to say the least, for those who get smoked by the Giant.