I can dedicate 2 hours daily for guitar practice. I want to play thrash/heavy lead and rhythm guitar. And hard rock and blues as well. Can anyone please share how do I divide my time so that I can work on improving my technical chops and work on genre study and writing.

Also how should I maintain a daily guitar practice log?
1) Find the John Pettrucci video/article where he talks about his approach ( folders for all the subjects etc.) - he lays out his methodical approach well and it might suit your goals. His Rock Discipline video is fantastic.

2) Blues and hard rock should be learned by ear - avoid tab for these styles as much as possible, because you need to work your ear and it's more difficult to learn metal by ear due to the speed and heavy distortion. Make learning by ear a daily priority - this is what helps you go from "guitar player" to "musician" and it will make writing and improvising much easier as well.

3) how you decide to divide your time is up to you, but with steady 2 hours per day practice you will be excellent within a year or two.

4) early Metallica is very accessible and a great place to start with metal.
For me, I just found out what techniques were used in my favorite songs and gave them 20+ minutes each.

Ex: This song has a dim7, major 1/3/5, and major scale runs.
I'd practice those slowly until I got up to speed and then I could play the song.

IMO the thing that is important is to do it slowly until your mind is numb, and then increase the speed slowly. You are doing it right when you get to the point where the solo is no longer enjoyable for you since you've practiced so much.

One time I literally practiced arpeggios for an hour straight, but I think this was a waste of time.
I'm the same as you, I have about 2 hours to dedicate to practice each day. What I try to do is, before going into a practice session where I have limited time, I pick about 3 or 4 things I want to work on for the day and then assign rough increments of time that I will work on each one for. So for example: 20 min alternate picking, 20 min on vibrato and bends, 40 min on applying theory to improvisation, 40 min learning a song by ear. And I change it up each day, depending on what exactly my goals are for each session. So if I were you, I would try to list various aspects of playing that I want to improve at and then cycle through a few of those each practice session. Based on what you said you are interested in, I think some of the things I work on would also be applicable for you.