The ones above? You can do those on any class, regardless of how squishy you are and regardless of whether you're built for PvE or PvP. Two exceptions:

(1) The Harvester boss in the Arboretum is a pain, because of it's healing mechanic. It helps being ranged when it shoots out it's feasts and / or powering through with a proper, high damage, PvE rotation.

(2) I'm talking about CP. If you want to do it in no CP, perhaps to have a lower chance of PvP, things get substantially harder and more tedious. Bosses one shotting you is a real issue (whereas at full CP not so much) and your sustain will suck. The best bet in no CP is wearing Imperial Physique, combined with something tanky. No doubt someone will boast they're doing it as a glass cannon, because they know all the mechanics. However, if you don't, it helps to combine Imperial Physique with something like Fortified Brass and Troll King. Still light armor, though, otherwise your damage will really suck.

The sewer bosses aren't much to write home about, easier than the ones above, with the exception of the patrolling horrors. The further inwards you go, the more powerful those get. Not sure whether they give you any achievement. They sure don't give you any rewards to speak of. I generally don't bother with them and can't really tell you what to expect. With their ground attacks, AOEs and pulls, all in a confined space, you may have to wear something tankier than usual, but that's about it, I think.

Yes. (Have done it.)

I'm a PvPer, so I run my PvP builds (various classes). This means DPS between 10K and 20K, because I don't do much more than weave my spammable. A nifty trick is to use an Infused weapon with a prismatic enchant, which will up your DPS substantally while just spamming.

Full Impen is IMO a must: You are in a PvP area, so don't be stupid.

Having either decent health (25K+) or decent resistances (1x Pirate + 1x Chudan on a light armor build) will mitigate potential one shots. Shadowrend may be a nice option, as you can afflict bosses with Minor Maim.

It usually takes me around 5 minutes to solo a boss, which is on the slow side. I've watched people do full PvE rotations - not my thing, I just can't do it - and finish bosses in 90 seconds or so. In that case, I am guessing, they were probably in full Divines PvE gear. Let's say you are a nightblade, you might get away with that, since it cuts down the time you are visible to other players as you go back into crouch / cloak after a boss. I can't see anyone but a nightblade or a streaking sorc do that and keep their Tel Var.

On magden, I run a magicka stacking build. Think about combining Necropotence with Crafty Alfiq, Bright Throat's or Spinner's and Bloody Mara or Citrus Fillet. I use 1x Domihaus + 1x Stonekeeper with that, prismatic enchants on the big pieces, magicka enchants on the small ones. That's a pure magicka stacking build for 50K+ magicka in CP. I get 51.5K magicka on my current build with Citrus Fillet, 57.5K after using Northern Storm. Using Atro mundus, so could have more.

The reason to stack magicka is, of course, to get a decent shield size. Your two most important defensive skills are Dampen Magic (not Harness Magicka) and Living Trellis. The latter is a phenomenal skill, which offsets damage you take, but also acts as a small burst heal if you reactivate it before it runs out. My front bar skills (Lightning Staff) are:

Cliff Racer
Inner Light
Bird of Prey
Deep Fissure
Dampen Magic
Northern Storm

Back bar (vMA resto):

Living Trellis
Radiating Regeneration
Bull Netch
Ice Fortress
Flex spot (Fetcher Infection)
Flex spot (Northern Storm - I really only use that ult, but could use something else this patch.

Yes, Bull Netch! Stamina for break free has to come from somewhere. Getting it from Bull Netch has the advantage that you continue to regenerate some stamina while blocking or sprinting. Feels great.