1 -- Regarding electrolytic caps - they contain a wet electrolyte and they dry out. As they dry out, the capacitance value decreases. Hotter the exposure, faster they age. Series resistance tends to go up as well.

2 -- Multiple types of tantalums. most prolific are the radial 'dipped' style tantalums. Tear drop shaped.
Also axial tantalums -- molded and solid.
Molded tantalums normally have a chamfered end to show end which is positive - most popular ones are often tan in color.
Solid tantlums look just like axial electrolytics except you will find the positive lead welded (actually usually cintered) so there will be a small metal bead at the positive end. Some are crimped on positive end. The solid tantalums tend to cost more than the other styles. Cost of tantalums has gone up since US congress passed the Dodd-Frank Wall Street reform in 2010 where they prohibit importation of 3TG materials (Tin, Tantalum, Tungsten and Gold) from the African conflict region countries. What that had to do with Wall street reform? Who knows ... but it seems to be one of the few rules remaining from that reform.

You can find pix of some of these styles on this page:
https://www.greatplainselectronics.com/products.asp?cat=40

3 -- no, they generally don't have a limited life span and will hold a value indefinitely as long as they aren't pushed too close to voltage rating. Downside to tantalums: They don't fail gracefully. Install one backwards or expose to excessive voltage can easily cause them to fail. And when they fail - they often fail shorted. When shorted - can cause nice little fireball or spark show. When used properly within the specs and give lead way to voltage rating - they'll last forever.