Overthinking "...expect there to be..."

This sentence struck me as odd when I casually said it in conversation:

I expect there to be bears.

...meaning I wanted [sarcastically] bears in the cave we were planning on exploring. What allows for the odd construction of "...expect there to be..."?

I scoured the internet, found an EL&U question, found another EL&U question, and discussed with my friends to no avail. Well, to some avail, but I'm still left with questions regarding construction, and how many grammar rules I'm bending or making up.

• The word "expect" always takes an infinitive clause (never a gerund [why?]), which explains the "to be". Could we say that "to be expected" is a verb phrase?
• I think "there" is an Adverbial Demonstrative Pronoun. Adverbial because it's supporting a verb and Demonstrative Pronoun because it's replacing the known noun phrase (the cave). I'm having a hard time backing this up with sources though.
• If "there" is adverbial, what verb is it supporting: "expect" or "to be"? Or, is it an entire verb phrase as I mentioned ("to be expected") that's been flip-flopped and split by "there", thus making "there" support both? (I feel like I just made that up but can't find evidence otherwise.)
• My friend said "there" is a post-position, because it's after the verb (he's assuming it's supporting "expect") but I read post-positions are not common in English.

Perhaps this is a daft and overthought, unimportant question, but it's been bugging me so I'm hoping for a smarter person to help with an explanation of this construction.

(A side thought, possibly unrelated, but regarding redundancy: If "there" means "the cave", I can say "I expect bears to be in the cave." ("I expect bears to be there.") This has the same meaning as my original sentence, but re-arranged. But I could even say "I expect there to be bears in the cave" or "I expect there to be bears there" which, to me, makes "there" redundant but still grammatically correct. Why?)

I don't think expect always takes an infinitive clause. Here's the definition from the Oxford Dictionaries:

expect

VERB

[WITH OBJECT]

1. Regard (something) as likely to happen.

   ‘it's as well to expect the worst’

   [with object and infinitive] ‘the hearing is expected to last a week’
   [with clause] ‘one might expect that Hollywood would adjust its approach’

   1.1 Regard (someone) as likely to do or be something.

   [with object and infinitive] ‘they were not expecting him to continue’

   1.2 Believe that (someone or something) will arrive soon.

   ‘Celia was expecting a visitor’

   1.3 Require (something) as rightfully due or appropriate in the circumstances.

   ‘we expect great things of you’

   1.4 Require (someone) to fulfil an obligation.

   [with object and infinitive] ‘we expect employers to pay a reasonable salary’

   1.5 (I expect) informal Used to indicate that one supposes something to be so but has no firm evidence.

   ‘they're just friends of his, I expect’
   [with clause] ‘I expect you know them?’

Note especially definition 1.5 -- this is the version you used.

So what you're really saying is my expectation is that there will be bears [in the cave].