1. My first question: is the problem of the 3E quadratic wizard versus linear fighter back again? Do I have to prepare for spellcasters trying to break my encounters?
Yes and No. Its entirely up to the DM in 5E.
The trick to DMing 5E from 4E is you need to understand that the classes in 5E dont all use the same resource recharge mechanic or pacing. Instead of at wills, encounter and daily abilities, the classes have a combination of 'short rest' and 'long rest' abilities. Its important to note that
not all classes recharge equally; some are long rest dependent (full casters, paladin, barbarian) and some are short rest dependent (warlock, monk, fighter).
What this means is, if you deviate from the expected adventuring day (6-8 encounters per long rest, with around 2 short rests taken in the middle) then this impacts the classes differently.
If you allow a short rest more than every 2 or so encounters, the warlocks, monks and fighters will dominate. If you allow less, they start to drop off. If you allow more frequent long rests (and shorter adventuring days) the full casters, paladins and the barbarian will dominate.
99 percent of the problems with 5E that I see comes down to many DM's dont get the rest 'meta' and/or dont police it strongly enough in their games.
Nova strikes were still possible in 4E (blowing dailies on the first encounter then pulling back to rest) and this is still a thing in 5E. Nova strikes tend to favor the full casters the most (who can dump the highest level spell slot).
I cannot emphasise this point enough. You need to get your encounter pacing and rest pacing right in 5E. Adjusting it one way or the other impacts on different classes differently.
I personally stick to around 6 encounters [[usually budgeted at 1 deadly, 2 medium and 3 hard] per long rest, with usually 2 short rests allowed during that time. I stick to this paradigm for probably 50 percent of the adventuring days the PC's encounter (sometimes there are less encounters, sometimes more). By sticking to this paradigm for around 50 percent of the time, the Players naturally pace themselves around this expectation, and police themselves accordingly.
5E is much more of a game of attrition and resource management than '1 deady fight per adventuring day'. Its more lots of little ones, each draining a portion of the parties resources until after about 6-8 'medium-hard' encounters they are out of hit dice, spell slots and other resources, and need to hole up to long rest.
Timed adventures (save the princess before X or bad thing Y happens, escape the dungeon before X or be marooned, recover the macguffin before X and you get paid double the gp etc etc) and 'random' encounters are your friend to enforce the longer adventuring days. Also reactive BBEGs who simply move the macguffin elsewhere if the PC's attack and then fall back. Use a combination of the above to enforce the adventuring day/ rest balance. If that doesnt work, and they still attempt to nova everything feel free to occasionally be more heavy handed ('You cant rest here, its too dangerous' or simply 'You rest but dont recover your spell slots' or if the players still dont buy in, 'No').
The longer AD's in 5E arent that bad. Compared to 4E, combats take a fraction of the time, and are over generally in about 5 rounds, with Player turns rarely taking more than a minute each. Most combats will be over inside of 20-30 minutes, meaning you can generally get at least 3 encounters in in a 3 hour session, and have plently of time for the exploration/ social pillars.
On the topic of combat, take note that 5E is much more swingy at low levels that 5E.
Finally dont worry about spell casters. They have cut down on high level slots in 5E (you only get one each of 6-9th generally), and the concentration mechanic is fantastic for removing the old 'pre buff' routine of having a million different spells running on you at once. Casters now have to be a lot more selective with their spell casting. Most save or suck spells allow repeated saves every round to avoid, and high level 'solo' monsters have legendary saves (auto pass a saving throw a few times) as well.
Youve made the right choice; 5E is the best edition of DnD ever IMO.