Are the giveaways bot-proof?

quick answer: if you're caught using a bot, you'll be banned.
And yes, people have been caught. Recently there was a wave of mass bans and blacklists for botting

It's easy to farm keys. This is why you shouldn't post plain keys

But it's easy to fool bots too:

DK7UW-6Y070-3FVUY
BKVDO-06MZE-WYB7S
1W7F4-TGKH1-Q4Z8F
VEM19-E78OA-AMNJ8
GQAMO-VZYLH-D3KP5
D22OY-IH4SR-XYLVO
XC4QQ-ZTZMI-HUFY1
DBNAG-WGLH3-RR5YE
J1OSC-YI25S-WC0BI
DFM1Y-W4N8T-J57LA

How could poor bots tell these are fake, muahahaaha....

glad you're having fun ...
but you didn't read the initial post - - talking about something wholly different than key-grabbing there...

Unfortunately, there're softwares that automate giveaway entries, whether by automatically entering giveaways by themselves, or just adding the "Enter Giveaway" button to the homepage for their user to click.

With people being generally lazy, and treating this site like a grab-bag for free games, it's only natural that such things exist.
They're forbidden by the rules, though, so users caught using them can (and will) be banned.

TL;DR

Giveaways aren't really bot-proof, unless they're created as invite-only.
And most bot/script users are level 0, level 1 at most, so making giveaways level 2+ or more would keep the majority of them away.

Quick answer: No.
However: Users who enter giveaways very quickly or send too many requests to the server will be suspended for 24 hours.

https://www.steamgifts.com/discussion/tqyrN/seems-like-people-who-use-auto-joiner-are-getting-banned-for-24-hours-edit

I think something Captcha-like would be good just in case. I get suspicious of seeing all the copy/pasted thank yous from the same people like "Rely thanx for gifway"
To me, I both hope they aren't a bot, and (this might make me seem mean) I wish they would put sincerity in the thanks instead of just pasting the same thank you, because it means nothing otherwise and is therefore only wasting my time checking the notifications.
Sorry if that last part seemed mean ._.