I gave my disabled brother who lives in a nursing home an echo dot.  It was set up with the alexa app on my phone, he cannot operate a phone.  The alexa app and the dot is registered under his amazon account.  If i load my family contacts (phone numbers) into the alexa app, that is signed on with his account, how do family member call his echo dot with their phones? It is an echo dot third generation.

one way is to install the alexa app on the phone.  in addition most amazon apps have the ability to to open and use alexa.   just call using it. 

Bought a new bluetooth speaker to connect to my Dot  and listen to podcasts/music in the shower.  For my previous bluetooth speaker, when I finished my shower and turned it off, the podcast/music would continue to play on the Dot.

For this new one, when I turn it off, the audio does NOT continue on the Dot for some reason. 

Is there some setting I have to enable to get it to continue playing the audio after the bluetooth speaker is turned off and disconnected?

So my brother has an echo 1st gen, the original one. It's not the dot or the plus or anything, and it's being fickle.

At first he tried to connect it to a new WiFi and had troubles getting past the Amazon-XXX. He tried looking for the "no internet" notification, and the more options section to click "yes" but found nothing. So, he did a factory reset, but I don't know exactly what went wrong. I think he mentioned seeing the color change from orange to blue, but it stayed at blue so he reset it again(again this is what i -think- happened) and then it turned off and back to blue and now no matter what you do to it (leave it plugged in for HOURS, try to reset, unplug and re-plug, use the action button) it will not stop from the startup ring light.

There is no official support from amazon for this device because it's outdated, i'm pretty sure the warranty is expired, and neither of us have found any help from looking for forums or sites talking about this issue, because there are none that say anything other than to reset the device- which is no longer possible. It's around $100 to buy a new one so we're hoping that we can fix this ourselves and get it working again.

The power chord is the original and the device has never been tampered with other than trying to get it to reset today.

who says amazon don't support it anymore!!!   they will still help IF you contact them and that is a fact. 

https://www.amazon.com/gp/help/customer/contact-us

So my brother has an echo 1st gen, the original one. It's not the dot or the plus or anything, and it's being fickle.

At first he tried to connect it to a new WiFi and had troubles getting past the Amazon-XXX. He tried looking for the "no internet" notification, and the more options section to click "yes" but found nothing. So, he did a factory reset, but I don't know exactly what went wrong. I think he mentioned seeing the color change from orange to blue, but it stayed at blue so he reset it again(again this is what i -think- happened) and then it turned off and back to blue and now no matter what you do to it (leave it plugged in for HOURS, try to reset, unplug and re-plug, use the action button) it will not stop from the startup ring light.

There is no official support from amazon for this device because it's outdated, i'm pretty sure the warranty is expired, and neither of us have found any help from looking for forums or sites talking about this issue, because there are none that say anything other than to reset the device- which is no longer possible. It's around $100 to buy a new one so we're hoping that we can fix this ourselves and get it working again.

The power chord is the original and the device has never been tampered with other than trying to get it to reset today.

The best way to do this is to have each location's Echo devices on their own Amazon account.
For example:

House 1: All Echo devices in this house will be on Bob's Amazon account. All smart devices will be set up on Bob's account and linked to Alexa with Bob's accounts. This includes light switches, garage openers, thermostats, alarm systems, smart plugs, etc.

House 2: All Echo devices will be on Larry's Amazon account. Same deal as above.

If you walk into house 1 and say turn on kitchen light, the kitchen light in house 1 will turn on. Since everything in house 1 is only setup with Bob's account, nothing in house 2 will be affected by any Echo device in house 1.