If that was my system the first and only thing I'd upgrade for certain is that CPU cooler. When you say an intake with an LCD I assume you are referring to an AIO with the LCD on the pump block? like this: NZXT Kraken Z53 240mm Water Cooling Kit - Black - Micro Center
They look good but are pricy, if you just want lighting then something like this would be great: Corsair iCUE H115i ELITE CAPELLIX RGB V2 280mm Water Cooling Kit - Micro Center
Otherwise a 5600X and a 3070 are a great pairing. Unless there's something you feel is definitely holding you back I wouldnt bother to change anything else.
You can use that, just note you'd have to front mount the radiator in your case.
It would go in the top, not the front.
From LianLi's own website about that model case, scroll down to the chart: LANCOOL 205/ 205M/ 205 Mesh - Tempered Glass Mid-Tower Chassis (lian-li.com)
RADIATOR Top: 240mm/ 280mm
So either the Z53 (240mm) or Z63 (280mm) will do fine
I assume you installed some software to set the little LCD on the pump? That software typically has a plugin to the motherboard lighting control which does the RAM and GPU lights. Now the NZXT software is controlling all the lights and that is its default scheme instead of rainbow. You just have to poke around in that software to find how to set those lights.
There's a few third party apps out there (as in not made by any parts manufacturer) that you can try.
https://rgbsync.com/ and https://www.signalrgb.com/ and https://openrgb.org/ are the ones I'm aware of, going to be personal perference on which one you may want to use.
Can you be more specific: Did you install the NZXT software for the AIO or not?
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