Hello and welcome to cycling.
The best thing you can do right now is just ride your bike and try to get used to slightly longer trips. When you put your body under stress it will adapt - just don't overdo it. Don't worry about weight training - it won't do much and the time you spend weight training is much better spent riding.
About your saddle - give it a few more rides and your butt should "toughen up". If it doesn't go away in a couple of weeks (assuming you're riding in those weeks) then you might need a different size seat.
Bike fit is very important - you can hurt yourself if the bike isn't set up correctly. Do some searches on bike fit to get some ideas - the main thing is having the correct seat height so you don't hurt your knees. What I do is this......I ride my bike and I put my heels on the pedals and turn them. If my legs go fully straight at maximum extension without me wobbling my hips to keep my feet on the pedals then that's about right.
Trip computers are a good tool - they aren't very expensive. I've seen them for $20 - $30. Cateye is a good brand, but almost anything will do just as long as it has the features you want. I wouldn't bother with "calories" though - it can't measure calories so it makes a guess and those guesses are usually too high.
Get some good bike shorts and a good bike shirt when you can afford it - you will be much more comfortable. Bike shoes too - but those can come later. And don't go out riding without a helmet - I know lots of guys who have crashed and wrecked their helmets and that's much better than wrecking their head.
Bike commuting to work will help - when I commute I try to go fairly hard since my ride is only 10 km and I want to get some exercise value out of it.
As you go on longer and longer rides you'll need to carry something to drink and maybe something to eat - you'll learn as you get more experienced. Rule of thumb is one bottle an hour on a hot day, although I tend to do a bit less I think.
Is it 110 km total in 2 days, or 110 km each day? 110 km over 2 days isn't really that far (neither is 110 km each day actually) although on a hybrid it will more difficult than on a road bike. You'll be able to do it as long as you get out and start riding.