To me it looks an awful lot like an old El degas. But although I have seen a few variations on their headstock shape, I am not sure i have seen a degas with that particular shape. But I am sure I have seen that shape somewhere in the dim past. Degas were the primary knock-offs in my area back in that time, not sure about elsewhere. As stated above, a lot of the knock-offs were made as contract work by certain factories, who would just take orders for x amount of guitars made on pattern x, with some minor variations. might be impossible to completely narrow it down at this point.

I guess the first thing I would do is assess the areas where there is the most damage. Try and identify what you absolutely need to do, before considering any of the cosmetic details. It is really hard from these pictures to narrow down work that needs to be done.

I would definitely fix any cracks in the neck pocket. You can probably do this fairly easily. You may have to gently pry the crack open in order to wick some thin (or thinned out, if you know what you are doing,) glue deeply into the crack. I love the Titebond products for this stuff. (The plain product is probably best for this type of work, rather than any of their specialty variations,) or maybe their hide glue variant, in the brown bottle.

Ceri set the standard, for repairing on his thread. Personally i would look on this as a learning project, and try to do all the work i could on it. However if your goal is just to get it playing you may not want to pour in the extra time to cover all the details, if they aren't actually vital. you may be happy with just tackling the structural damage, and hiding the other flaws.

measuring tools are your friend at this point. Unless you are prepared to fill holes and redrill, you are going to need very accurate measurements in order to find replacement parts. Especially for your bridge. depending on the age of your guitar, and the factory of origin, you might be measuring in metric. if you do choose to install new hardware, you still need to do some accurate measuring to place it.

If you can't find a drop in replacement bridge, which might be likely you will have to plug the existing holes, and redrill.

At this point you may have to do so much work, that you will have to consider dealing with the finish. Now if this is a lacquer finish, repair and touch up work isn't too out of the question. But you will have some work cut out for you in matching colours, and blending. If it is a poly finish, then blending can be a lot trickier.

You may even choose a complete refinish, and that is a whole separate operation. A bridge to cross when you get there.

I guess to sum up:
Identify your repair goals, how much time effort, budget,and hassle you are willing to devote to the project, and what your expectations are for the finished project.

Identify key areas that MUST be done, no matter the goals. Are there structural damages, like the neck pocket crack, or a separating top, that have to be repaired, and aren't just a cosmetic or trivial defect? What parts need repairing or replacing? What do i need to buy, or maybe manufacture?

then you need to assess how much other work will result as a byproduct of the work you plan to do. IE will the repair work mean doing other work? Will you be able to fix this without marring the finish, or without creating other woodworking?(will you need to do some cutting to be able to access damaged areas, for gluing etc, and then have to patch?)

heh long winded to be sure, but there's probably a lot more to think about than I have mentioned.

Your best bet for plugging the holes in the neck, and body are to clean up the existing holes. Then make some mahogany(if that's what the body is,) dowels of the appropriate diameter. in fact you might be able to buy some doweling that will fit. Plug the hole, trim, then carefully sand flush.

You may want to put in a Nashville bridge. it is a modern variation of the Tune-o-matic.

there are all kinds of wiring mods for an LP. You might want to look into using push/pull pots and coil splitting the humbuckers, or phase switching, or...

Good luck and keep us up to speed.

I know i haven't updated any of my posts, but I kinda picked up some temporary extra work, so I haven't been busy with my projects