After my message yesterday I ordered the replacement battery, and all the three recommended tools. The Phillips and the Tri-Point screwdrivers as well as the spudger. I almost didn’t believe it: this morning, before nine o’clock, DHL was here already with the parcel. The tools are of an excellent quality and I needed all three of them, but within less than 20 minutes the replacement was complete and, against all odds, the MacBook runs again. And to answer your question about the trackpad: mine oozed out by 4mm. But no problem. From the inside the trackpad is held by two thin and short metal stripes, each one fastened by four tiny little screws. Probably the tiniest screws I ever handled, but also here the scPhillips Screwdriver was perfect. Those metal stripes were severely bent bent but could be pressed flat again and I re-mounted them upside down so that they could hold the touchpad perfectly again. Much easier than expected, but obviously a 100% success!
Harriet - fortunately I read all the comments and questions - including yours. Otherwise I would have described exactly the same problem:
My early 2011 MacBook Pro’s battery is so swollen, that the touchpad sticks out of the keyboard and even the underside of the laptop became curved instead of flat. I wonder whether you got any reply from iFixit? I am afraid to buy the new battery and tools today - only to find out, that more parts need to be replaced which were destroyed by the swollen accu?