#1: Yes, That would be if the Dallas was a 1285 or 12885 as they had no internal battery. The 12887 does have the internal battery and there are not connections from it's battery to the socket pins (where the x85 series does have those pins). I see a x87 in your socket (if that is your exact board picture) so NO.
#2 Most external batteries were not rechargeable back then BUT that would depend on what the manual says about the ext. battery. Some did use an Lithium or NiCad rechargeable but most were just Alkaline packs. You would have to check it if supplies about 5v at about 10-20mA at the pins. Also the Dallas x85 has a cmos clear function thru external jumper (think that may be what they are talking about on JP13).
added: the 12887A also has the same pins to clear cmos as the 1285/12885

You would have to cut the RTC outer casing and cut the positive connection to its internal battery if you want to connect a external battery. I got 2 of these boards and I know access is very limited to the RTC from the top sitting between the isa and pci slots.

Unfortunately desoldering the RTC is prob what you need to do. Then install a socket, modify current rtc to have a button battery or make the headers for external battery

Remove the RTC and install a socket it is then.

How tricky is the RTC to remove? It is kind of adjacent to the ISA slot, but I don't think it has any nasty solderpads on the ground plane or anything? A solder wick and solder sucker should be enough?

I socketed both mine, when I was pretty bad at soldering I spent hours with a solder sucker and a soldering iron sucking out the joints and eventually did it nearly damaging the board.

Second time with improved skill and a proper desolder gun with a station took about 30 minutes. There is 1 or 2 square pads that were tougher then others but generally it was pretty straight forward.

Old solder can be tough sometimes too