These concerns are valid and you should proceed with due diligence. I recommend to not install any piece of software which you don't trust on your work pc. Install it on an unused computer instead or use a virtual machine (virtual box from oracle is free), then your safe. A check for viruses with virustotal.com is also a good idea.
The Byteball wallet is open source software, so it's integrity can be proven quite simply. The wallet will gain trust over time. The more users download and run this wallet without issues, the more trust it will gain. It must be several hundreds now, a lot of legendary btt members among them, who know the usual altcoin scam. And the real identity of the developer is known and we've already seen his face in a video. IMHO we're pretty safe with this software!
It's not the wallet as such, it's the bot. When you click on the link to the bot you authorise external software to run and this is in addition to the wallet itself.
yu can use androïd wallet to link yur btc if yu have feer..it is similar pc wallet