1. there are a lot of reasons this could be happening that I can think of. off the top of my head:
a.) your demo is slow. the optimal rollout should get him there in time to at least get 1 early sticky on any aggressive scout and several on their soldiers, hopefully deterring their aggression somewhat.
b.) your demo doesn't have enough scout protection. he needs at least one and maybe both scouts with him to deny soldiers or aggro scouts.
c.) their demo is going flank. this rollout WILL get you there before the other demo. if their demo is going flank and wrecking yours, maybe try sending yours flank as well.
d.) they're overcommitting just for the demo kill. just counterjump your soldiers, have your scouts shoot their sollies in the air, and clean everyone up.
2.) I think that, when your demo goes choke, it can be useful to wait until their soldiers jump and then counterjump. it doesn't matter either way if their soldiers just jump their side, but if they jump yours that counterjump really helps. I don't think gullywash is really a map where your soldiers should be completely denied by scouts- if you're jumping your side they won't be there, and if you're jumping their side I'd have your demo with you and a scout rush up onto their side once your soldiers get there, so their scouts shouldn't be able to deal with you anyways.
3.) unless you specifically plan a mid fight where your med stays valley and players return to him when they need heals, he NEEDS to basically run up a side as soon as he gets to mid. unless one of their soldiers does a fast gunboats rollout, his life shouldn't be in danger if he just moves his ass. have him go up left elbow for sure if your demo rolls out choke (unless your combo rolls out choke as well, which btw is a viable option if your demo is fast/does a lot of dmg), and PROBABLY have your medic go up right aggro if you all go lower (although you could do a more passive climb up the left elbow from lower, I just don't usually do that).
4.) on the bridge. they probably don't need to go choke because I'm pretty sure going flank and jumping up the awning or straight onto the point via the log is faster.
5.) rolling your demo out through flank is often a very good idea, especially if their demo is doing a lot of damage to your combo. if their demo goes choke, your demo should get early dmg on him, then you can commit to killing him. if their demo also goes flank, just take over their side and they'll take over yours, and start from there (I'd prolly initiate aggression onto them with a soldier jump over the pt).
6.) nipple is a good position, but I wouldn't always take it right away cuz you can be so easily counter jumped. what I would do is, if both teams have kinda taken a side, jump 1 or both soldiers on nipple or past it directly onto them, then have scouts and demo follow up and dunk on them.
some of this is just based on how I like to play mid (aggro soldiers -> cleanup scouts), but whatevs, hope it helps