Why is there is no comma after "yet"? What does it mean compared to "however" and "but"?

"Yet" may be thought of as a synonym of "however" or "but," neither of which would be followed by a comma in the two examples you've given; however, if it follows a semi-colon (as in this sentence), it does require a comma by common convention.

Yet has a slightly different meaning to however or but - both of which are assuredly negative with respect to what precedes it, whereas "yet" is only slightly or partially negative, and does not need a comma (not for this reason, just for syntactical ones).

Yet nearly always implies that the second (negative clause) is not fully justified or explained by the first (positive) clause: "She was really well off, yet she refused to have any work done on her house."

So in these contexts, it means "but still ...", so "yet still ..." would be tautologous.