Lead-acid battery charger, specific circuit, 3~4.5 Amps, doubts + recommendations
I want to build a lead-acid battery charger


Stop stop stop.  

It turns out battery charging is really hard to do well.  

Lead-acid batteries are fragile, actually, and take damage from almost any kind of abuse (and even normal use). A less-than-ideal battery charger will destroy a lead-acid battery in months, and SLAs are even more vulnerable. 

The only thing that really works properly is a 3-stage battery charger.  These are complex enough that homebrew designing one as a starter project would be madness - you could spend months on it.  

So the battery charging problem should be solved with a prefab module from a competent supplier, that performs full and proper 3-stage charging.  Save your valuable time for the meat of your project.