Remote will only start when i am close to vehicle

sounds like you have a weak battery in your remote starter, you need to have checked out

Could you please tell what brand or describe the antenna and remote.there are several brands of remote starters. Few are interchangeable.

That sounds normal foe some

You really need to be more specific if you expect some assistance with your problem. What's the make and model of your remote starter? What's the year, make and model of your vehicle?

There are two types of starters for Dodge, if you installed new battery, check to see if the remote start is to ignition module or starter solenoid, then make sure the circuit has not been closed-they go in series circuit!

To operate the remote starter, press and release the green trunk/key button on the remote twice within two seconds like so: press (thousand one), release. press(thousand two), release. Wait. If you press the button too fast the unit will only read it as one, especially at greater distances and, you may actually start the car and shut it down before it even starts.

Check the hood pin switch. It's located under the hood around the edge of the engine compartment. It's designed to make contact with the hood when the hood is closed. Also, check for a remote start shutdown toggle switch under the dash.

The vehicles makes a clicking sound when using the remote starter? Does the vehicle make the same sound when attempting to start with key? If so, this sounds like an issue with the vehicle not having enough power to start the car or, there is an issue with the vehicles starter.

The problem you have described do not sound remote start related. A remote start unit does not have the ability to alter the RPM. The remote start system only replicates the process of turning on the ignition, starting the engine and keeping it running for a predetermined length of time.
The heater temperature problem should not be remote starter related either.
As for the day time running lights, although rare, if wired inproperly there is the possibility that the remote starter has caused it to fail. This will have to be determined by a qualified technician.

If the remote starter it was working before, check that all the doors trunk and hood are closed. And remote start the vehicle, approach to the window to see if the dash board lights turn it on if it does; check the pin switch make sure when you close the hood the switch get closed too if this is Ok. Check the tack wire you?ll see it is coming out of one of the ignition coils.