Can I use a 25 foot HDMI cable with my Roamio OTA 1TB DVR?

I have a few questions.

I will be getting a Roamio OTA 1 TB DVR in a few days. I have gone on line to read the Start Here green poster. It says to connect a HDMI cable from the Roamio unit to the TV.

Here are a few questions:

Note: My TV is a Samsung UN32J525DAFXZA. I am using a DSL modem and it is a technicolor C1100T-802.11n Wi-Fi Router.

1. Is it possible to send a signal to the TV using Roamio’s Wi-Fi and the TV’s Wi-Fi?
I believe the answer to this question is no.

2. Could I use a 25 foot HDMI cable to send a signal from the Roamio unit to a TV in another room?
If the answer is yes, please tell me what type of HDMI cable I need to get.

Note: I just bought a GE 3 foot HDMI –HDMI-TO-HDMI cable. The cable supports 5.1 and 7.1 channel surround sound and high speed 10.2 Gbps. I am assuming this 3 foot cable is O.K. to use with the Roamio unit and the TV. The cable is also certified for 1080P FULL and 4K x 2K ULTRA.

3. Or do I need to use a TiVo Mini?

I would like to replace the 3 foot cable with a 25 foot cable when I want to use a TV in another room.

Please provide the following information on the 25 foot HDMI cable:

1. Where to buy the cable.
I am assuming Amazon would be a good place to start. How about monoprice.com?

2. What would be a good price for a cable?
I am thinking less than $20.00 (Amazon price!).

3. What specs. should I be looking for on the cable?

4. What would be a good brand to get? And yes I know that if I go through Amazon the brands are iffy at best.

Any help that you can give me will be greatly appreciated?

Thank you.