For (1), yes, you can certainly do that. The only case where it might be a problem is when it's a very high-bandwidth controlled-impedance signal, but if it's a high-bandwidth controlled-impedance signal it's not going to be on the edge of a chip anyway.
For (2), this can cause manufacturability issues. I recommend you look up the term "via-in-pad" for more information; in short, the via can wick away solder during reflow, leading to a poor solder joint. There are ways to get around this when you need a via in a pad, but they add a lot to the cost of the board.
Also, if you are having thermal issues with a capacitor to the point that you need to consider heatsinking it, you're almost certainly doing something very wrong.