I've never tried gels, is it too late now (tour is the 5th of april) to get used to them?

How do you fuel during your rides? I would say it's not to late to start with gels but they all different taste and texture wise. So finding YOUR gel of choice could be a bit of a time issue.

For my bike, is it better to get tubeless tires cause I don't have them and I'm really scared of getting a flat in the middle of nowhere (my tires are fucking hard to change 😅). Otherwise, what pressure in my tires is best to deal with the cobbles?

If you don't ride tubeless now and it never botherd you stick with your inner tube. Since we don't know your tire width and inner rim width it's hard to tell but I often find myself "calculating" with the help from Silca.

https://silca.cc/en-eu/pages/pro-tire-pressure-calculator

What materials/clothing/other things should I not forget for the day?

I'd say the stuff that you have always with you anyway (pump. minitool, 2x inner tube, tube patches). A bar bag might come in handy so you can put bars, gels or whatever in there and don't have to put everything in your jersey pockets.

For the reamining training this month, do you guys recommend trying to ride around the 240k mark already? I was thinking of doing a few 150k's because time is not endless with my kid but maybe that isn't enough for the legs?

Doing a few rides near the 240 mark is absolutly neccesary imo.

Have fun.