I bought a B2B charger and was really glad I did, as it charges about 5 times as fast as any other split charge relay. I bought this one...
https://www.12voltplanet.co.uk/sterling ... v-30a.html (that will tell you more about what they do.) I don't bother with hookup much, so it's great to have. I find that with about an hour's driving each day I'm on holiday, and reasonably careful use of my electrics, I don't need any other charging source, even with a fridge.
Yes it will charge your battery and run fridge at same time (well mine does easily!) when the engine is running of course.
Basically, you need to think about how much time the fridge will be running with the engine off (discharging your leisure battery). This is a tough one, as the amount of time your fridge runs will depend on the fridge itself, the ambient temp, ventilation, etc. I reckon mine runs about 20% of the time normally when in use. You can then work out (along with other electric you will have) how much electricity you might use (in Amp-hours) in between running the engine. This will help you work out what capacity leisure battery to buy - but to be honest, if I were you I would get as big a one as you can fit in. Ideally you don't want to discharge your battery more than 50% to keep it healthy, plus all batteries will lose about 20% of their capacity over their first year - so I think of my 120Ah battery as just 50Ah.
So... if you reckon you will use more than 50Ah without running your engine, you would need mains hookup (or solar) to charge your leisure battery as well as the B2B charger. Note that the B2B charger only works off the vehicle alternator - so for mains charging you need a mains charger as well!