Sounds like you have a lot of things figured out now, Rythm, but I'll chime in with 2 thoughts

1) It's totally possible to gain 5 pounds for no reason. The upside is you usually lose them for no reason too. If you get on the scale every day you'll get used to the fluctuations - mine are usually in the 2-3 pound range but 5 isn't unheard of... If you play the daily weigh-in game make sure you're mentally able to deal with the UPs and the downs, because fluctuation is normal.

2) Sounds like you're making progress on the treadmill - just take it one step at a time. Add either 5 minutes or push the speed or the incline up just a little bit each week. Personally I think setting weekly improvement goals are better than every session, but it's all opinion. There is no "right" way for you to exercise - and with exercise (especially with weight loss as a goal) it's about CONSTANTLY changing it up. Your body will adapt and get more fit & you'll need to do new exercises or make the ones you're doing now a little harder (by making them longer or more difficult). Little changes will add up. You're clearly on the right track!