Alright you are asking a lot of info so I apologize in advance if this is long and rambley, I'll do my best to be concise with my thoughts. As far as your first problem dealing with quick attack, ESAM recently posted a video about specifically dealing with that move.
https://www.youtube.com/watch?v=Ew1iSalGmTQ that is the link to that video. I would also suggest following/subscribing to ESAM being that he is the premiere Pikachu player. TL;DR though the video basically says that lingering hitboxes are the best thing to deal with quick attack. So for Mario, your Nair is your best friend, short hop nair when he is quick attacking you will stuff the quick attack hit box with your nair. However, be sure not to fast fall it, the hit box has to stay out as long as possible. A lot of Mario players get into the habit of short hopping into fast fall nair as an approach and it leads to them being programed to always fast fall when they nair so don't fall into that.
The next problem, in terms of killing your most reliable option is to read them into an up smash. As far as guaranteed kill setups for Mario down throw into fair at the edge is true at certain percents and certain levels of rage depending on the weight of the other character. landing up air into forward air is also guaranteed from like 60-90% and of course this means down throw --> up air --> fair is also guaranteed. Of course reading them into F smash is also a good option but up smash is more reliable because it kills off the top.
As far as using cape on Pikachu's thunder jolts, it depends on how often your opponent uses it. If they are super campy and spam it a lot I wouldn't try to cape it very often I would try to master power shielding it instead because if you approach and power shield it you can often have enough time to get in and punish them. If they are using it sparingly then you could try to cape it more often. I also like to try to challenge their camp with fireballs, if you get good at the timing you can cancel out the thunder jolts and often they will get hit even when you get hit as well which basically means you trade and you don't get punished and it changes their mindset so they know they can't just camp you. This is SUPER effective when you have the lead, never mindlessly approach them when you have the lead they are the ones that have to make something happen. But this is advice for every matchup not just Mario vs. Pikachu
Anyway hope this helps!
