Some thoughts...
1. I keep one of those cheap 'outlet testers' plugged into the galley's outlet to see if our AC power is correct any time we hook up to shore power...
2. Mexico uses 60hz everywhere we've been over the years - I thought 50hz was a European thing...??
3. The DC charging feature on most small inverter type generators is only rated at about 10 Amps - using this feature will take LOTS of running time if your batteries are depleted - I use the 1.5 'rule' for recharging - if your 80 Amp Hr battery is 1/2 depleted, you'll need to 'pump' 40 amp hours back into it for a full charge; using a 10 amp chg'r, 40/10=4 (hrs) x 1.5 = 6 hours on the charger...! You'll be much better off finding a higher rated AC powered charger for quicker recharges...
3.1...Charging from your 7-way tow vehicle's system isn't much faster that the above, due to the small wire sizes that limit available charging current..this works on the road when you have hours & hours of travel but not very good for trying to recharge when you're stationary just idling your vehicle...
4. We use those power strip protectors for all our major components plugged into Ac power inside our AS - TV, Sat receiver, DVD player into one...Microwave & phone chargers into another - while 'open ground' protection may be questionable, these devices do protect your stuff from voltage surges or spikes - I've seen them 'blow' at home when we have power outages restored with BIG power spikes...
5. It's true, electronic device prices seem much higher in Mexico - You'll probably be $'s ahead to just replace your microwave & converter/charger when you get back across the border - or - the converter might have an internal 'fuse' device that's blown and would cheaper to repair...
Hope you're having fun down there, otherwise...