I’ll offer what help I can. The first video could have went real bad for you. Do NOT throw her fire ball that close to a downed opponent, it’s not safe at all. Gauge your distance properly when throwing them. Also Chun has amazing walk speed compared to Paul so playing footsies or out poking him shouldn’t be too hard. On the subject of pokes, I feel like you’re missing her best poke st. mp. You use cr.lp which is good but it’s even better when used in conjunction with cr.lk, standing mp and cr. rh. Seriously standing mp is too good not to use, you can link it off of cr.lp’s, from there you can cancel it into lk/MK hazanshu, lk hazanshu will be -2 on block and mk hazanshu will be neutral on block. The mk hazanshu sets you up for even more offensive opportunities provided your opponent doesn’t have a 3frame normal (Chun Li does, it’s her cr.lk) or a 3 frame reversal. Your other option after the mp is ex kikoken, which is +8 on block, that also allows you to continue to pressure your opponent. You can also choose to simply block, walk back or backdash…seriously what is Paul gonna do besides cry.
Next I’d suggest learning her BnB’s find one for yourself and drill it into your game. If you can land/confirm off of cr.lpx2 then you can chain into cr.mp, first hit of cr.hpxx Ex kikoken into follow ups, an easy follow up would be mp into boost combo. You can also link Chuns back mk, mk launcher move after her cr.lp into a decent damaging combo, especially with Juri on your team I’m assuming. check the respective combo threads for each character.
Chun Li has good/decent anit airs her neutral jump rh, which I see you use, air to air hp, or mk. Standing mk, and df.lk, the last option leads to a combo. Just gauge your spacing well and use the appropriate move for the jump in. Also air to air, I doubt that Paul beats Chun…in fact I’m sure she smokes him.
As far as approaching, you can still walk behind lp kikokens when thrown from the right distance. She has a great forward dash too. Remember she doesn’t need to get in your face to be in, she has good enough walk speed to walk right into st.mp, fp range. In your second video you fought Zangief like this, I would just say be careful on that approach cause he does have some great normals. I’ve been stuffed by Gief before in a footsie war. I use cr.mp against lariats, hell I use cr.mp against hadoukens also, nothing better than going under a shoto’s fireball and tagging them with a combo, but that’s about the only time I use that poke.
Anything else just ask and I’ll see if I can help, provided you found this post even remotely useful.