Epoxy. Gorilla Glue is exterior rated, but makes a mess, a big mess if you use too much as most people do until they get used to it. Your instinct to avoid nails or screws is good. It concentrates stresses and almost always does more harm than good.

I couldn't find any extra long patio tables when I looked a while back, so here's what I did instead. On one patio, there are two matching tables and 12 chairs that can be used separately or together. They're aluminum framed tables and the chairs have mesh sling type seats (no cushions) so they dry quickly. We've considered adding a third table, but so far have managed without it. For the adjacent sunroom, I found a maple table (Queen Anne style) with two leaves that extends to 10 ft. and 8 matching chairs. The finish isn't trendy at the moment, so it hadn't sold even after the store owner recovered the chairs and I got a great deal. The sun room is large enough to accommodate a another table, so I bought an 8 ft. folding banquet table and a fitted cover in a linen look fabric from TableVogue. I liked it so well that I bought a 6 ft. table and fitted cover, too. The smaller table is useful for setting up a buffet on the patio. For the large folding table, I bought 8 simple wood chairs on clearance that can be stored stacked in pairs, along with the folding tables, in an upstairs closet. If I wanted to use the folding tables outside, I might check out the folding chairs at Ballard Designs when they go on sale. Maybe someplace such as Pier 1 or World Market would have similar folding chairs. The ones I looked at, while not made in the US, were at least not made in China, and I like the look of them better than the metal folding chairs I recall from childhood. It sounds sort of cobbled together, but when similar table linens are used and the tableware & flowers match it all works well.

You will not know until the rollers are at least exposed. I don't understand what you are asking. Yes I have worked on sliding patio doors dozens of times. The worst problem I had was no parts available because what I worked on were in apartment houses and cheap. It's best having one person in charge of keeping the door from falling while another retracts rollers. Raise bottom rollers so door drops then lower top rollers until door will tilt out of frame. Lay door on a table or saw horses to inspect. You can then tell if bearings are shot or can be cleaned and lubed. Use graphite to lub,oil and WD40 atract dirt. I would call around to see if rollers are available before taking door out in case rollers fall apart.

There are people/companies who do restoration of all kinds of stuff including china and ceramics. My mother had a porcelain figure which had some damage and she had it fixed by a professional restorer. You can't tell where the restoration was unless of course you are someone in the industry who is extremely savvy and looking for restoration since that impacts the value of antiques. You could start by calling a local museum and asking to speak to someone in their conservation department. Or call an antique store in your area and find out who they might recommend. It is not cheap to have it restored professionally but it generally is worth it if the piece merits the expense because it will look as good as new. You might also cross post in the Antiques and Collectibles Forum. Although it's not an antique, people conversant with antiques would probably know how to find a restoration place in your location.