The best ways on how to deal with bugs, especially ticks and mosquitos
I'm based in Australia, so my experience is different from most on here; basically mosquitoes and other biting insects are dealt with by insect repellent. I use a brand called "Bushman" which works for Ticks, Leeches, Mosquitoes etc. It's not the nicest stuff (you end up with an oily film on your skin, and it's awful if you sweat it into your eyes), but it works.
Edit: it comes in 20, 40, and 80% DEET. I generally use the 40%, and haven't had any issues.
How to deal with wild animals
I'm only likely to get attacked by snakes, so I wear canvas gaiters over my pants. They also protect against thorns and branches that would otherwise snag your clothes/legs.
How to better calculate how much food and water to bring on a hike
I calculate minimum of 2 litres per day, ideally 3. It will depend on weather conditions, and the terrain, as climbing hills will make you sweat a lot more than strolling through meadows. Always have 2-4 litres left in your vehicle. You can push through the last hour or so thirsty if you know there's water waiting for you.
A Lifestraw or similar water filter is a good investment, as you can top up your water supply on the trail.
If you need an actual knife, you really can't go past a Mora Companion (especially the stainless model). The keep a great edge, and are cheap enough that you can abuse them with a clear conscience. Strong enough to baton firewood if you need, but small and sharp enough that you can skin and butcher a deer if you want to.
If you're not in need of a "real" knife, that weight and space might be better utilised for a multitool. I'd recommend the Leatherman Rebar (not cheap, but it has a 25 year warranty, so it's a good investment).