New Groupset

Or have some very nice 8-10s wheels you want to keep...

*correction* You can run 11s on an 8s freehub if you remove one of the single cogs and spacers from the middle of the cassette, and use a thinner spacer onboard of the new, shorter cassette. But that leaves you with 10 cogs with a big jump in the middle and is a faff. Less so than machining the freehub and cheaper than buying a converter cassette from edco. It's basically a dodge if you want to go to 11s but can't afford to upgrade the wheels yet.

An 11 speed cassette won't fit an 8s freehub. It's possible, but very unlikely, that giant used an 11s hub and spaced it to 8s as has been suggested. You should be able to fit 10s to an 8s freehub (tiagra 4700 is very good), but if the group set is really on the way out then I'd expect the wheels and hubs to be showing their age before the mechs and shifters. You may need new wheels anyway. New group set plus wheels would be a lot to spend against a second hand/last year spec new bargain. The question is whether the frameset is worth upgrading, kept with lower spec kit as a spare/winter bike or sold/part-exed for a new bike... 

Wheels - if they are 11-speed compatible, I'd expect that there are currently a few spacers behind the current cassette. Are there?

I know my Fulcrums used the spacer supplied plus 1-2 further, thinner spacers to get the 8-speed cassette to fit and not rock. To fit 11-speed, you just remove the spacers. 

Pics would probably help of the BB. However, if this is the bike:

https://www.giant-bicycles.com/gb/2013-giant-defy-4--compact--2013

It looks like square taper, which will be threaded and easy enough to replace with Hollowtech.

I've just replaced the 2300 groupset on my first road bike (Spesh Dolce) with a mix of Tiagra and 105.  However, I've only done this as the old groupset had done about 20k miles and was simply knackered and barely functioning, and I had spare bits. Tbh, I'm not certain the Defy 4 frameset is worthy of this upgrade.  Financially, it may be better to buy another bike with a better groupset, swap the stock wheels with your Quests and use your Defy as a runaround.

The Defy 105 is pretty cheap second hand. Might be better off selling your one and putting it towards a newer 2nd hand one with 105.

To answer your questions:

1. More than likely not as the jump from 8 speed to 11 speed is large. There is not enough room without the lockring being outboard of the end of the axle so that the freehub would not turn when clamped into the bike.

2. This is difficult to answer without knowing your current bb model and/or crankset. BSA threaded BB's have various models to fit 22mm (SRAM), 24mm (Shimano) and 30mm crank spindles.

And inspect the BB bearings. If rough/pitted or has flat spots replace with new. Also be sure you use 11 speed chains as the chain OD is narrower to accommodate the 11 speed cog spacing.

Hope this helps.

What year is your bike? I have a 2016 Defy and the bottom bracket is BB86, not threaded.