Which direction should the antenna face?

From what I have read, it wants to be vertical. So either up or down. But I must report that I stopped using this product months ago. My opening distance kept decreasing until I was often back to right in front of the door. Now some days it was 150 feet, and others only 20 feet. RF is a strange "animal" and many things (that you certainly can't see) interfere with it. My current solution, which is still showing marked improvement, is a simple, home made, parabolic reflector installed on the original opener antenna. Found it on the internet - freeantennas.com. I'm pretty convinced that I have a "weak or faulty receiver" as I watch my neighbor open his door from 200 feet around the corner. But I continue to look for cheaper solutions than replacing the motor unit or circuit board, which costs more than a whole new system.

Would this antenna extension kit liftmaster 41a3504 work for sears craftsman 139.53753 315mhz?

Yes. You can see my review as my garage door opener operates on 315 Mhz. This will work on any garage door opener in the 300-400 Mhz range. Most likely though, you need to get the antenna outside of door, like I did. However, there was not enough cable in this kit to run the cable on the path I wanted to get outside. Antenna should be mounted vertically, up or down.

Why is the grounding required.. is it for safety or does it improve the reception? is it required if the ariel is left doors?

All Radio antennas need some sort of ground ...to me it was very easy to ground it off the bracket thats holds the motor ...very simple

I have 2 door openers will 1 antenna hook up to both doors or will I need a separate one for each door?

Since you have two openers you have two separate controllers; one for each opener. So you will need 2 antennas. We had 2 antennas on our 2 openers and they worked great.

Will this work for liftmaster la-400 and la-500 driveway gate operators?

This antenna kit is for the receiver. It has nothing to do with the operator. Your receiver should have an "F" connector on it to accept this antenna

User Manual LiftMaster 41A3504-1 Antenna Extension Kit for

LiftMaster 41A3504-1 Antenna Extension Kit for Garage Door Opener - Use Manual - Use Guide PDF.
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Owner's manual - (English)

Installation Instruction 433MHz Receiver Logic Board Antenna Extension Kit

WARNING: To prevent possible SERIOUS INJURY or DEATH from electrocution, disconnect power to opener BEFORE proceeding.

The Antenna Extension Kit model 41A3504-1 was designed to work with the 433MHz Receiver Logic Boards

This kit contains an antenna, coaxial cable, adapter and an antenna bracket.

After replacing your receiver panel, follow the instructions below to access the logic board connector and install the antenna extension.

Installation

1. Screw the threaded end of the adapter into either end of the coaxial cable.

2. Plug the smooth end of the adapter into the connector on the logic board. The connector is located under the “Learn” button on the rear panel of the opener.

3. The antenna bracket can be mounted inside on the header, or for maximum range, outside the structure. Route the coaxial cable accordingly.

4. Attach the antenna and coaxial cable to the antenna bracket as illustrated.

5. Mount antenna bracket so the antenna is unobstructed and away from any metal or steel.

NOTE: Do NOT modify or remove the existing antenna.

See other models: G885LM G373LM 886LMW HOMELINK RPTR 041A5034

User Manual LiftMaster 41A3504-1 Antenna Extension Kit for Garage Door Opener

Installation

Product Infomation and Reviews - 41A3504-1 photo

LiftMaster 41A3504-1 Questions and Answers

Owner manual PDF of LiftMaster 41A3504-1 Antenna Extension Kit for Garage Door Opener.