Had my current gear for few years now.

Ibanez s570b, Peavey Vyper 30w and Boss ME-70.
Currently trying to part them to save up for my new gear.

already sold my ME-70 and still looking to find new owner for the amp and guitar.

Over the years I've find myself more into Hardcore/Metalcore stuff.
so I decided to get ESP H-1001 and a 5150 or 6505 head + cab.

gonna get used for both. hopefully to get the guitar for around $450
and amp + cab for $600. I've got a lot of digging to do.

few questions :

1.Will I see improvement in the sound if I upgrade from current gear to this ?

2.Since I'm blowing all my money in to the guitar and amp. I wont have a effect pedal. will I be fine ?

3. Since I'm in college right now and living in a apartment. Should I just get the guitar and an interface + effect simulator and output the sound from my speakers? (6505 head + cab might be too loud for apartment?)
Ibanez S570B WH
Peavey vypyr 30
Focusrite Scarlett 2i4
Well i have the exact same gear you are looking to buy.

1. Yes, a very big improvement.

2. Yes and no, the tubescreamer (ibanez TS-9, TS-7 or maxon 808) is a must. They are not very expensive and it's like the most important thing

3. head + cab will definitely be too loud if you want to hear the good tone. You can turn the volume really low (below 1) and you will be able to play in an apartment, but really the sound will be a little muddy and not as good if you play on normal volume (at least 1.5 or better 2).

So if you are playing in a band or planning to pay in a band in a near future i would recommend to get a head + cab, because in rehearsals you can crank the volume up. Otherwise i don't really know.
I'd recommend the 6505 1x12 combo for your situation. Plenty loud enough to gig with, you can run ext. cabs with it, and a little more manageable when youre trying to keep quiet. Cheaper too, it can be had used for around $400. Just a thought.
1. Yes you will hear a difference

2. a Tubescreamer type pedal is really nice to have with

3. Yes a nice guitar and maybe a POD HD would be very nice. You can also use the POD when you get an amp

I highly doubt you can find a 6505 head and a decent cab for $600, the head alone will cost that. $500 if you get a great deal. A decent cab will run you $300+ used
2002 PRS CE22
2013 G&L ASAT Deluxe
2009 Epiphone G-400 (SH-4)
Marshall JCM2000 DSL100
Krank 1980 Jr 20watt
Krank Rev 4x12 (eminence V12)
GFS Greenie/Digitech Bad Monkey
Morley Bad Horsie 2
MXR Smart Gate