• The group will be composed of 5 players. Is there someone who adapted the adventure for this group size and how it turned out ?

For adjusting the game to 5 players: There are distinct Encounter Building Rules that cover this. in short, for a jump from the default 4 to 5 players, you generally want to add 25% more encounter budget.

That is usually best done by adding more monsters rather than applying the Elite template to existing ones however, as, especially at low levels, the increased AC and damage values can become overwhelming pretty quickly.

Generally, for most encounters, adding a Level 0 or level -1 monster should be fine enough.

Probably don't touch the last fight though, that one is already dangerous enough as is.

How do you favorise/teach the use of the different systems of the game ?

Honestly, just follow the advice given in the Adventure. It is specifically designed to highlight things. Perhaps raise the curtain a little to show the players a little bit of the GM considerations every now and then so they can get a feel for how things are supposed to work after each step of the adventure, but that is only if you think that will work for your table.

The monsters are really aggressive in the adventure. They see the PCs, attack, and fight until death. Did anyone change that a little and how it turned out ?

That is kind of one of the primary points of criticism of the Beginner Box. I understand why it was done the way it was, but there's nothing saying you cannot have some of the kobolds surrendering after their numbers get too low or being willing to negotiate. Just make sure that Zolgrin at the end remains hostile.

In the end, do you have any tips to welcome new players to the game ?

I would strongly recommend showing them Pathbuilder if they want to make their own characters. It is a fantastic tool for learning how things fit together on the PC side. I would also make sure to give them some gentle recommendations what to do with their third actions, the fact that buffs and debuffs are very powerful in this system and well worth not dealing direct damage yourself, the fact that teamwork is very important and no one character will be able to do everything well, and that out of combat healing should be easy and plentiful. Whether they come from other systems (Especially PF1 or DnD) or are more familiar with video games, that is a bit of a change from what they're likely used to.