Solar panel regulators

Directly from the supplied regulator should be fine.

Probably OK except the regulator supplied is likely to be very basic and therefore may not be ideal for your particular battery type and it won't be MPPT, so won't get the maximum harvest that is possible.
It is also better to have the regulator as close to the battery as possible.

Cheers,
Peter
OKA196 motorhome

Yes, safe but not that efficient probably. Bulk charge takes 14.6 v and more and a basic regulator (ie PWM) fixed to the panel doesn't deliver it IME so the battery never properly charges.

It's worth swapping to an MPPT regulator set close to the battery as Peter mentioned particularly if you're in cool to moderate climates. Victron do units with some charging smarts.

Hi
Regulating a solar panel output twice is counter productive

If your panels come with a good PWM regulator that's all you need to start with, just check the quality of the PWM controller though as there are some pretty cheap and nasty ones out there.

Both PWM and MPPT can provide the same charge voltages so nothing to gain really from that perspective, a MPPT is more efficient though in that it keeps the solar panel around its max power generation point for example:

PWM using 2 x 120W panels in parallel:

2 x 120W panels, ISC = 7.26A, IMP = 6.72A, VMP = 17.85V
Two panels in parallel (PWM), questimate 7Ax2 = 14A@12V=168W, 14A into battery

MPPT using same two panels in series:

Two panels in series (MPPT) = 6.72AX35.7V= 239.9W, I=P/E 239.9/12 = 19.99A@12V into the battery.

Above assumes no loses, please forgive any errors.

A good quality MPPT can supply more charge current when the battery volts are low, the gain decreases as battery volts rise, if your thinking of using a multi functional unit ie DCDC charger with solar input your not going to get the same efficiency as you would out of a high end MPPT unit.

Looking from a different perspective though you could probably buy three panels and a cheap PWM to give you 21A into the battery for less than the cost of the MPPT setup.

There can be other advantages of using a MPPT with series panels, ie smaller cable, more output under low light conditions, get the most out of what already installed etc, its all a balancing act.