TL;DR
Sprinting, medic items. Also machine guns and hard blocks as maybes

The medic weapon should be switchable with the grenade and will only heal others, not yourself. It should heal at 5 or 10 points at the speed of the spade. I think this should really encourage team play which is what this game is missing. Alternatively every player could get this item and not have to switch it with the grenade, but im not sure if you want players having more than 5 items (too cluttered).

Sprinting should be 1.2~1.5 times normal run speed and you would have a higher jump cooldown meaning it would not go up hills less than a slope of 3 or 4 blocks. After jumping you would have slow down to normal speed for 0.5~1 second. Falling would put you to the same speed as it would were you walking and fell (depending on how this feels you could give a speed boost here too) This would encourage the making a of roads and tunnels which i think is a good thing. Obviously you would not be able to shoot while sprinting and should not be able to shoot for a small amount of time after sprinting.

A couple of other suggestions i'm not sure will make the game better.

One mounted machine gun per team: This would spawn at the HQ and would take 2 people to carry (maybe only one if this feels bad because of jumping) and would slow you down considerably. You would also have to crouch jump to get up hills (like getting out of water). the machine gun would have to be planted and would have to be brought back to the HQ to resupply ammo. It would also be destroyed by grenades making it spawn back at the HQ. (maybe after a period of time)
It would take time to set up and take apart discouraging one person from just moving around wherever he goes and keeping it a defensive weapon.

Hard blocks : Would cost 10 blocks to place and have maybe the durability of 3-5 blocks.

Not bad ideas, Although needs some review.

Sprinting is taken out of EVERY SINGLE MODERN FPS.

I don't like any of these ideas.

i dont like the "one mounted gun per team". a gun placed by a single person to be crewed by anyone else would be great but put a cap on it like 1 gun per team on smaller servers while on 16v16 6 guns per team

i think the hard blocks idea is great. Bullets shouldnt be able to make any damage to it at all.

Just because sprinting is in every fps doesn't mean it is bad. Look at it on how it will be a benefit or a detriment to the game. I feel it takes too long to get to the front lines and i like the idea that people will need to build more roads so you can get to front line faster.

Are there any reasons it shouldn't be in the game? I should add you wouldn't be able to sprint while carrying intel. This i think makes the game more balanced because once a guy gets the intel out of fog range its impossible to catch up to them.

I think you may be right pieman, maybe the server admins would be able to pick the number of MGs. I just felt that one MG on a hill can over 25-50% of the front line. so 4 MGs could completely cut the map in half and would be a nightmare for Green if they got one on every hilltop looking into the swamps.

that hard block idea is very creative, but maby a shorter cost would make more cense cuase with a 10 block cost you will only get 5 hard blocks out of it every time you visit the command post-tent thingie.

Thats the point. You should be able to build forts out of hard blocks without a lot of work or it would be over powered. People should be using normal blocks for most things and hard blocks for supports or windows.

yeah i like the "harder blocks" and the "medic" idea too

but instead of having "hard blocks" how about "improving" blocks with some tools ? you hit the block and it will last longer (capped at maybe 3x durability ?)
kinda like a reverse pike

+1 To medic items.
Another good addition would be a pair of binoculars.

Actually what would make the game perfect is if they could prevent hackers, and maybe a shotgun, an actual sniper, and an ak47, m4a1, or any rifle.