I've been in hospital and I've had crisis team.
Hospital is useful for keeping you contained within their 4 walls, fed, and on drugs. It can be a bit scary though and the staff are usually very busy. Sometimes it's helpful to meet other people in the same circs as you though, although there will be others with very different issues, and many people there against their will.
Crisis are more helpful if you are willing to engage with them- they actually have people you can speak to. Last time I avoided hospital by actually using the crisis team properly i.e. phoning them when things were really hard. You can do that any time of the day or night. Sometimes it's just helpful to chat to someone….about anything that takes your mind off negative stuff.
I don't know what 'red' is. It depends on the way they do things. Could be a particular team, area, referral stage etc.
They do bloods and ECG as standard. Can't remember why- someone explained it to me once and I know that my funny heart rate that they found was mentioned in my notes. I suppose some physical problems can have similar symptoms to mental and they have to rule out physical reasons? And maybe some drugs are contra indicated by physical stuff. E.g. don't give beta blockers to someone with a really slow pulse 
Might be an idea to perhaps try a home visit. It's not like they invade your house. They don't have uniforms, no one would know that it's not a friend popping around. They won't go roaming all over the place. Usually they come in, sit on the sofa and have a chat, go away again. Or help with some tidying up etc.