Wiring problem on 4 gang metal light switch
You didn't mention what gauge the wires are, so these answers are generic:


Yes, the ground wires should be tied together although there is some debate on whether this is required by code. In this case all the ground wires should be connected together in this box, and the neutrals should all similarly but separately be be connected together (note: don't mix the grounds with the neutrals). Since you will have only two remaining devices in this box, this should be fairly easy. Collect all the ground wires from any Romex that enters the box and bond all of them connector with a wire nut. (See note about wire nuts sizes below.) Do the same for the neutral wires. For grounding, look to NEC sections 250.148 and 250.148(D) Since this is a metal box, make sure there is a "ground pigtail" connected from a ground screw connected directly to the metal box to the ground wires (which you are bonding together in #1 above), as shown in this example.
The color of the wire nut and the specific manufacturer's instructions tells you how many conductors and of what sizes each nut can be used to connect. But generally speaking, 6 or more conductors is not advisable: it's just too easy for one to come loose. If you need to connect more than 5 conductors, I would recommend a "push-in" wire connector, of which there are 2-, 3-, 4-, 6-, and 8-wire variants. Your particular situation should be aided by your question #3 (below) which will reduce the conductor count.
If you have switches which you're sure no longer control anything, just remove the switches and cap the wires with wire nuts. Make sure you've disconneced the hots from the others that are feeding live devices. (Leave the ground connected.) Opinions will vary about whether to keep the neutral bonded to the others. I tend not to.


A few more notes:


The Code requires that non-functional switches are removed and replaced with blanks. You should be able to find blank inserts to fit into 2 of the 4 gang slots.
Wire nut colors are standardized, but depending on the shape (wings or no wings) and the manufacturer's instructions, some wire nuts hold more than others. I've never seen more than 5 wires successfully in a wire nut that didn't merit replacing. :-)
There are rules about how many conductors and devices can fit inside a box. If you post the size of your box (usually marked in cubic inches inside the box) and a new diagram once you've removed the two left-most devices, we can confirm whether your box is filled or over-filled. At first glance, what you've got seems pretty tight (i.e., likely over-filled according to code) with 4 devices. When you remove the 2 switches, that may change.
Whether to keep the neutrals separate is a little more complicated. For the above advice, I've assumed all of these switches are fed by one circuit from your panel. If not, let us know and we'll advise how to handle the neutrals.