Is my anonymity at risk in the following scenarios?
Not particularly, if you follow the basic guidelines.
1. I am using other browsers or programs (accessing the Internet, but not through Tor), while I am using the Tor Browser;
This shouldn't affect your anonymity: the traffic generated by the Tor Browser will go through the Tor network, while the traffic generated by the other browsers/programs will follow the regular path.
As I said, this shouldn't affect your anonymity: you must kept your identity using Tor and the one using the other browsers/programs separate!
Indeed, the information you provide while using the Tor Browser can be used to deanonymize you if it is correlated with the information the other browsers/programs provided. This means that you should avoid visiting the same websites, using the same accounts, etc.
Assume that you have two accounts on a website:
- public_account -- this is your official account, the public one that you access through a regular browser, and any connection available.
- private_account -- this is your secret account, the one you want to keep private, that you access only through Tor.
From a very restricted technical point of view (analyzing packets' content), your anonymity seems safe, as long as you don't send any information about yourself (or about public_account) with private_account. Unfortunately, analyzing the packets' content is not the only toy in the attacker's playset.
There are many scenarios possible, let us choose the one where the attacker is the website owner (or, the website has been compromised). The attacker knows:
- Your public_account;
- The fact that the private_account owner is using Tor.
It can be enough to break your anonymity if he does some statistical analysis1 between the private_account and the others.
- It's strange, they are always connecting at the same time;
- private_account and public_account often interact together;
- private_account and public_account never interact together;
It is very hard to blend in against statistics, because trying too hard can have an ironic effect.
A question has already been asked on the Information Security community, about using the Tor Browser and a regular one side by side; you can get more information by taking a look at it.
2. I am using a torrent client to download files (not through Tor), while I am using the Tor Browser;
Your torrent client is just a program accessing the Internet. See 1.
3. I am uploading files using the Tor Browser;
As usual, it depends of what you are uploading. Is there anything in or related to these files that could provide information on you?
The only thing the Tor Browser will give you is an anonymous way to upload the file.
4. I am downloading files using the Tor Browser (from cloud services, e-mails, file sharing services, other sites).
The Tor Browser won't protect you against what you have downloaded. Downloading files always creates a risk for you and your computer. Tor (and the Tor Browser) won't protect you against that.
In other words, any file you have downloaded can potentially be a malware that could deanonymize you, as well as it could encrypt all your file (ransomware), or do something else. This is independent of Tor.
1 It is not about one or two specific point(s), it's about the whole.