Canon doesn’t say anything explicit about Nora’s assumptions on Cas’ relationship with Dean in either sense.
End of the answer. Now, going off topic… Do I think Nora thought Dean was Cas’ ex? Even though that’s in the realm of headcanon, I think it’s possible she did.
Canon also doesn’t say anything about Nora’s assumptions on Cas’ sexuality, but since her behaviour with Cas was ambiguous, I believe writing her actions off as just randomly atypical is not the most logical explanation.
Let’s look at her behaviour, keeping in mind that as a premise she is well intentioned, not trying to deceive, and socially capable within the norm.
NORA [to Cas]
Where have you been all my life? […] You’re not like the other sales associates. There’s… something different about you.
I can assure you, there’s – there’s not.
I know these things. You’re… special.
1. Nora is someone who thinks she can read people well, sense how they are on a deeper level.
2. Nora has just complimented Castiel, which will complicate things in a few seconds.
Hey, Steve? I found this in the supply closet. Do you know whose it is?
Um… That’s mine. Thanks.
I also found a rolled-up sleeping bag behind the tool locker.
Yes, I wanted to be thorough with inventory, so I worked late last week, and taking a nap here was easier than going back home to my bed. Which I-I have, of course – a bed…and a home.
Wow, Steve. You’re so… responsible.
3. Feeling that she has a deeper connection to people, Nora is prone to basing her interactions on subtlety and (assumed) shared knowledge.
As a working single mom, it’s hard enough to get a date, let alone meet a really great guy. And … tomorrow’s my night off, and I know you’re off, too, and … I was just wondering if there’s any chance you’re… free tomorrow night?
Um… Yes? Yes.
NORA gives him a kiss on the cheek.
You’re the best!
4. First, Nora complains about her love life (“As a working single mom, it’s hard enough to get a date”). We assume it’s to convince Cas to date her, but we later find out she never intened to ask Cas out. She told him about the hardships of being a single mother to convince Cas to babysit for her.
5. Then, she adds that it’s even harder to find “a great guy”. She’d just complimented Cas about being especially great, so we assume she’s referring to Cas: “let alone a great guy like you”. Since we now know she wasn’t asking Cas out, she must’ve felt comfortable enough to tell a man (who’s not a close friend) how hard it is to find other decent men, meaning she was most likely expecting some sympathy. Seriously, it’s getting ridiculous.
6. The way she phrases it when she asks if Cas is free can’t be interpreted in any other way than her asking Cas out on a date (in fact, we assume that’s what she just did). Unless she feels free to phrase her request in what would normally be such a misleading way because she assumes Cas will know she’s obviously not asking him out due to some kind of shared knowledge.
7. Nora concluded the interaction with what, in that context, is yet another overt sign of romantic interest (the kiss). If we assume she’s interested. But instead Nora must’ve done it assuming that, once again, Cas will know that can’t possibly be meant romantically. Because, evidently, Nora thinks both Nora and Cas know something about Cas that won’t make Nora ask him out on a date, and won’t make Cas think Nora is asking him out on a date. [Laughter from the audience ensues.]
8. She tells him in a friendly manner that he’s the best, which maybe makes Nora come off as a little desperate while we’re still assuming she asked Cas out, but which we understand in hindsight as her thanking him for the favor Cas just unknowingly agreed to do her.
So, if we mantain the premises that Nora isn’t trying to deceive gratuitously and isn’t really damn socially inept, the most logical explanation to why she acted like this, to me, is that she tought Cas was gay and thought that Cas knew that she knew.
Not to mention that I picked the script apart for the sake of precise analysis, but if you randomly pick an out gay man from a crowd of out gay men, there’s a 90% chance that he can recite these lines by heart, without having ever seen them. The way Nora interacts with Cas here looks absolutely deliberate, but I doubt Berens would be oblivious to its implications once he’s done it even if it’d happened by accident. Which I strongly suspect it didn’t. Just like the double entendre about ‘batting for the other team’ when the two extras are conversing in the shop didn’t.
Worth noting that even though Nora’s aim is not manipulation, Cas here is agreeing to something thinking it’s something else, which plays, if lightly, into the theme of consent and deception.
But in a cool way because the things I got about Berens so far are:
1. he can double-code
2. he WILL double-code
3. he’s got the technique
4. he won’t shut up - seriously, you can try and make him
5. he’s a little shit
6. DOUBLE FUCKING CODING THE QUEERER THE BETTER
WHY DON’T YOU UNBOTTON THAT IN A TOTALLY HETEROSEXUAL WAY WHILE I HETEROSEXUALLY CHECK VERY THOROUGHLY THAT YOU LOOK ALRIGHT BECAUSE I PLATONICALLY WANT TO MAKE SURE YOU DO AFTER I TOLD YOU I CAN’T LET YOU GO ON THAT DATE FOR COMPLETELY HETEROSEXUAL REASONS MY DEAR ASSUMED-UNINTERESTED-IN-HETEROSEXUAL-DATING FRIEND WHO DOESN’T BAT FOR THE SAME TEAM AS THOSE TWO ASSUMED-STRAIGHT GUYS I N A DEFINITELY SPORT-RELATED SENSE edit: BUT PLEASE DON’T DIE LIKE THOSE OTHER PEOPLE WHO’D BEEN DUMPED BY THEIR BOYFRIENDS OR LOST THEIR SPOUSES