Essence Eater as a position 5 when you're planning to max Mana Drain is the correct choice.

Maxing Mana Drain is effective versus the enemy heroes both in lane and in the game, and especially with AM as your carry, so that was the right call.

However, instead of taking the 20 MS talent at level 15, you could've taken the lower Hex CD first.

As for the level 10 talent, the bonus slow when you're playing around Mana Drain and shard (which you should've had sooner) can be worth it, but the MS is not bad either, so this is not really a mistake.

Boots first as a pos 5 is too greedy, you need more regen to be able to trade hits and also to give to your AM so he can stay on the lane. Starting with a stick also is not a bad idea vs an Earthshaker + Silencer lane, so something like: Magic Stick, Tango, Salve, Blood Grenade, Branch, Sentry (540 gold)

No reason to upgrade Magic Stick to Wand so early at minute 6, you could've instead spent that gold on Rain Drops / Wind Lace / more regen

Blink first is standard and fine, but the 32 min Agh's afterwards was completely pointless and borderline a grief. It's not your job to deal damage this game, you and your team could've benefitted way more from: Glimmer Cape & Force Staff for more mobility and survivability, Shard to drain more heroes (you have AM on the team after all) and not get interrupted by a random Fissure or Cask, Lotus to get rid of Global Silence

Ghost Scepter for survivability is ok, but enemies literally bought 1 dust in a 56-minute game, so a Glimmer Cape probably would've done way more work in terms of keeping you alive, AND it can also be used on teammates

0:30 should start on the left instead of on the right, also, the first Earthspike should be used to secure the ranged creep unless you can hit both enemy heroes at once.

There's little room to maneuver on the right, and with the way the creeps are positioned, it's also much harder to harass the enemy without drawing creep aggro. There's no reason to be there unless Lotuses are coming up or you're planning to use the gate.

2:24 could've been a great half pull but you walked too far to the right so it was a full pull and your creeps just stayed alive. Also, not a great time to pull since you can't contest the lotus at min 3

2:53 Try to stack the small camp and then pull it, that way you can deny a full wave

5:25 waaaay too aggressive of a yolo dive, no reason to tank creeps.
You should either be securing the 6-minute power rune for mid or the 6min lotus and preparing for a fight at the 7-minute wisdom.
It kinda worked out with the Lich TP giving AM a double kill, but there was no reason for you to die there.

9:45 you see AM is on his way to have a fast Bfury, enemies just died, your ult is on CD, no reason to just stand around you should go and start making stacks in the jungle

12:00 don't TP back to lane anymore, save your TP's for fast reactions and just walk instead.

No reason to keep sitting around AM, he has Bfury and now he wants to farm, so you have to start playing with everyone else in the team but not with AM.

17:00 instead of wasting ult to KS the Silencer, you should've first disabled the WD so he can't interrupt you guys, and after that with an Earth Spike + ult + some damage from Pudge, that would've been an easy 2nd kill. Instead, WD lives and you both end up dying because of greed.

17:57 another wasted TP, just WALK INSTEAD! This happens a lot throughout the match.

19:20 you should stay top where you have vision and play with your cores.
It's way too optimistic and unrealistic to TP and catch a low HP Earthshaker there, there's no way he stays for over 20 seconds on the same camp so that you can reach him

28:40 as mentioned Agh's is terrible here, could've had a full Lotus Orb to completely counter Silencer's Agh's ult

Throughout the game: you tend to blink way too close to enemies, yes you should blink close enough to use hex & earthspike, but there is almost never a reason to blink into melee range of them

Sometimes it can even be better to save your blink and walk up to enemies to use earthspike or hex (esp. When you have bonus cast range from your neutral) so you have your blink ready after to reposition