1. Is there any way to replace a dead Flanged carto from a tank without having to empty the tank first?
Yes, it's possible to replace an old carto with a new one without completely emptying a tank -
How to "Hot Swap" a Carto in a Cartotank. You will need a
Slap Yo' Mama Adapter : Big Daddy Vapor to do this though.

Slap Yo Moma tank accessory tool
It's an excellent idea to get one of these tools. Not only will it make changing cartos and filling your tanks much easier, it will also protect your tank's important o-ring seals from being damaged. I find owning one of these to be indispensible.
PBusardo's Review/Demo of the Slap Yo Moma tank tool
Until you can get one of these tools, though, you will likely need to remove the remaining juice, save it in a small container (old medicine cup or small dish). Prime a new carto and setup your tank like you would the first time.
I don't know what method that you have used, but I'll include my
Cartotank Setup Guide, which has step-by-step instruction and a video demonstration.
2. What to do if you want different eliquid, do you have to toss the carto and start with a fresh one?
(I used a vivi nova before this which was very easy to rinse, refill, put in new flavor etc. Tanks seem like a lot of work)
Well, cartotanks are different from clearomizers because the carto has polyfiller in it which retains the flavor in it. If you choose to add a similar, say a fruit flavor for another fruit flavor, you would not need to change cartos. But adding a fruit flavor to a tank that had something like a desert or coffee flavor in it, you'll likely get strange results.
Most tank users end up having multiple tanks, each with their own flavor in them. I often have up to a dozen tanks going simultaneously, each with their own flavor. I use the less expensive
IBTanks instead of the Phiniacs. You can get two IBTanks for the price of a single Phiniac. I made a vape gear budget where every month I ordered a new tank from IBtanked and therefore I had a dozen tanks over a years time.
Cartotanks do take a little more time to setup, and do have a learning curve. However, using a good method of tank setup and a little experience makes things easier each time you do it. I much prefer cartotanks for their fuller flavor production over a clearomizer, and they have very little maintanance other than juice refills once set up.