The acid has to react with the minerals in the concrete, but any residue of paint or plaster will prevent or reduce penetration and reaction in that area. It will not look good. You're on the right track with the buffer and pad, but you'll need a cleaner/solvent too.

When I was thinking of doing a stained concrete floor, I bought the manual and video by Gaye Goodman, which is comprehensive and excellent. She recommended a soy-based solvent called Bean-e-doo to remove all paint, glues, plasters, etc.

I can't remember all the details, but she recommends at least 2 people to apply the stain. It was something like, the first person either wets an area or pours a diluted solution on an area, and the second person spreads. You want variegated, but you don't want blotchy, which can occur if you don't get a fairly even wet coat on the area quickly. She also may cover the stain with plastic bags to slow evaporation so that the reaction has a longer time to work, based on the results of her color testing. You must wear protective gear, and you MUST carefully protect walls, trim, etc. from the acid splashing.

She often gets a beautiful variegated effect similar to marble, and has a technique for creating "veins" in the slab as well.

I did not stain any floors because I found out our subfloor is gypcrete, not real concrete. But I can recommend her manual and video as comprehensive training from a pro who does beautiful work. She says some of the most beautiful, marble-like results are on aged slabs like yours.

She explains how to seal the floor once it is dry. The most durable sealers are epoxy...but I don't know if any of these are suitable for DIY. Oil-based sealers are more durable, deepen the color, and add depth. Water-based sealers are also available. She discusses her experience with different brands and products.

I have her Fundamentals manual, Artistic Acid Staining manual, and How to Stain DVD and would be willing to sell them if you are interested. I'm not here to sell anything, don't care if I do, and don't want to get banned. I'm just throwing that out there in case you're interested; I would have been back when I was wanting to stain my floors. You might also want to contact her to find out if content has been changed or updated recently. My materials are several years old. BTW, when I was researching acid staining, I scoured the web and found little info. Only 1 other book beside Gaye's materials was mentioned, and I couldn't find it. Nowadays, Melanie Royals of Modello Designs might have some information as well. She does acid-stained "carpets" with her stencils.

Here is a link that might be useful: acid staining how-to

Absolutely agree with andersons statement that anything left on the surface of the concrete will look awful when the stain is applied. I have stained concrete several times and used a scraper to remove residual layers then scrubbed the floor with the large black pads on an electric floor scrubber rented from HD, but I wet the floor first then scrubbed. It really removed everything. Be careful about anything you use that is not water based on the floor because it can soak into the concrete and block the acids reaction.

I have always used Kemiko brand acid stains and have been very happy with the results. They have a very good website that can give you some good additional information. Their products have been around for decades and they really know their stuff. The last time I used it I just put it in a spray bottle to apply it being careful to mask off anything I did not want it to get on. You can always keep adding more layers to deepen the color if it dries too light.
Good luck.

I have only stained new concrete floors but, even then, have been pretty meticulous about cleaning them before hand. I have used only Brickform acid stains in Amber, Caramel, Jade and Turquoise. For a sealer I use a Davis product called W1000 (waterbased sealer) then usually many coats of Durawax. I will attach a link to our kitchen floor, the most recent one we've done. This is the only floor where I have used an integral color (Buff, by Davis Colors) in the concrete and then stained it. We live in sand country and I have noticed that over the years (even with pretty good but not meticulous care) the sand does wear the stain off of the concrete.

Here is a link that might be useful: acid stained kitchen floor