I had problems getting mine out too. I gave it a really good dose of oil and applied it by standing the machine at a 45 degree angle with a towel supporting under the fly wheel so it didn't topple over. About 20 mins later I put the machine on it's side and again supporting the back, oiled the spool race from underneath the machine. Leave it for an hour or so and then then try again. The base assembly may never have been dismantled from the day it was made. If all fails try WD40 overnight. I know it's a bid no no in some quarters, but it has worked for me in the past. Old oil could well have congealed sealing the base assembly to the plate at the back.
The thread that was caught in my machine I had to pull out from underneath, but I couldn't see it until I had taken it apart. The chap in the video makes it look so easy, but mine was a bit of a struggle and as I said before, was a B.... to get the base assembly back in position to move the gibb hook to line up with the screw hole. I was just about to put the needle plate back when I realised the pointed bit wasn't between the two bits at 12 o'clock, so had to start again
If all else fails, Maidstone Sewing Centre may be able to help, as I notice they have quite a few Featherweight machines on the shelves in their home page.