Is this negative pole grounded correctly to chassis? As you can see there is an additional ground cable fastened to the chassis. Should i use another gauge for this?

Negative pole seems loose. All connections should be tight. I don't like the neg. battery cable clamp that I see and have used. The wire clamp rarely tightens satisfactorily and even if it does, the exposed wires corrode under the clamp. Your local parts store will have a battery cable with a chassis ground wire.

What about the smaller wire with yellow terminal that is fastened to the firewall in the chassis. Should i replace it also with a thicker gaugr wire?

 Use the ground wire on the new cable you're about to buy. The ground wire on the new one will be substantially smaller than the battery cable, much like your existing one. The wire size is fine. 

  On 1/16/2019 at 7:35 PM, Mark Maras said:

Negative pole seems loose. All connections should be tight. I don't like the neg. battery cable clamp that I see and have used. The wire clamp rarely tightens satisfactorily and even if it does, the exposed wires corrode under the clamp. Your local parts store will have a battery cable with a chassis ground wire.

I turn the bracket around to get a tight connection. Is this fine?

 It will probably work for a while but two things need improvement. The first problem is the wrong size connector on the chassis ground wire to the cable clamp. The weak link in that style battery clamp is the exposed, bare copper wires at the end of the main cable. The wires will start to oxidize very soon. The oxidation starts under the clamp, unseen. Replace the cable with one that has a dedicated ground wire. Probably less than $25.00 at your local parts store. You'll be glad you did. One less thing to screw with and another item checked off the list.

  On 1/19/2019 at 7:23 PM, Mark Maras said:

 It will probably work for a while but two things need improvement. The first problem is the wrong size connector on the chassis ground wire to the cable clamp. The weak link in that style battery clamp is the exposed, bare copper wires at the end of the main cable. The wires will start to oxidize very soon. The oxidation starts under the clamp, unseen. Replace the cable with one that has a dedicated ground wire. Probably less than $25.00 at your local parts store. You'll be glad you did. One less thing to screw with and another item checked off the list.

Just sourced this one.  Thanks for your recommendations mark. I accidentally blew the fusible link shrink wrap off so maybe will order one if needed.

Where do those heater hoses go? I've never seen that before. Or don't you have a heater and those are A/C?

No heater. I removed that crap. Ac hoses