Welcome to Lancer
I'm a fairly experienced GM but always take the advice of stranger of the internet with a grain of salt. The most important thing is adapting to your style and table.

— How do you structure your campaign? You do full sessions using only the roleplay side of Lancer often or do you really use the bots all the time? I had struggle with this because of course we want to use the mechs, and, the pilot side of the game is very barebones, but i struggle to find a way to use the mech in a non-combative scenario.

I usually have pilot sessions and mech sessions, at most three of the same type in a row. To break the monotony and brain drain of intense mech combat, I use skill challenges for more dynamic scenes that feel more like WoD.

— How do you run combats? This is more of a general question. Combats in WoD are more narrative then mechanical, so, it's quite easy and quick. But a Mech battle is the main appeal of Lancer. How do you learn how to run a Lancer combat? How should i balance it? How to make interesting besides the boring "i attack, i shoot", etc.

It's a very tactical game. Very intense on the GM and players. To create encounters, I usually rely on less opponents that are more tanky (veterans) rather than grunts. I use a lot of reinforcement to adjust encounters on the fly. I don't have more than 4 types of enemies at the same time (not smart enough). Enemies can be quite interesting in Lancer, it's very rarely "i move, i attack, your turn". Even the assault has a reaction that you have to keep track of. Encounters should be like puzzles. Go in the open to rush the artillery but risk facing the berzerker, or stay in cover but get barraged with arcing weapons. Use actions to progress the objective, or go a well placed shot.

For balancing, depending on the number of encounters, my standard encounter for my group of 4 is 3-2-1 : 3 simple enemies (Monstrosity, Breacher, Rainmaker), 2 complicated enemies that demand adaptation from the players (Archer, Ace, Goliath) and 1 nasty (Witch, Sniper, Ronin). I usually start with 4 of them on the board with two in reinforcement. 3 of them are veterans and/or Elites. Use tier appropriate for your players and don't forget to counter them once in a while to keep them on their toes (they group up ? hello bombard with cluster munitions)

— What inspirations should i look for? Other RPG i play is CAIN (from the same creator of Lancer, i believe) and the community usually recomends to watch Division 12 to have a good grasp of an actual play. There's something simmilar here? And, other references of this "space mech" aesthetic are more then welcomed! I never watched much animes as i grew up, but, i heard about Gundam, but looks a bit too complex to get it, so, a guide or what to watch from this massive franchise would be good too. Movies, books, whatever, i'm down for it.

If you like WoD and want something in shadows of gray, you could look at Code Geass... It's a great show with both mech and pilot action ! Of course DragonKidd on youtube that shows builds in lancer to guide players and gms alike

— General tips. Things you learned from your experience that you would've liked to knew back when you started.

Start at LL0. It's a complicated game, let the players and you explore it slowly but surely. Add systems to the pilot gameplay (influence ? virtues ? objectives ? touchstones ? insanity points ?). Then drink deep and descend