For your first question:
Yes, your audience can emotionally connect with your characters in third-person POV. It just depends on how you write. If you are a good writer who knows how to write good characters - you should be fine.
However, you do need to watch out for passive third-person POV. Passive third-person is more of a past tense, which is less engaging than a deeper sense of third-person.
Like Erk's example comparing:
He wondered where the birds had gone.
Where did the birds go?
Like the second example, you want to include lots of character thought to help provide a more concrete perspective of what your character is actually thinking and their opinions- to help the reader understand and eventually develop 'emotional bonds' with your character.
Doing the above and having strong, well-developed characters, will help your reader care about your characters.
For your second question:
It is a possible choice to have a perspective in 1st and a separate perspective in 3rd, but it is not your best option.
If you have 1st and 3rd perspectives 'switching off' it may get confusing, and your reader will end up lost and will jumble up characters. You could still do this, but just work hard to clarify things so it is 100% clear who the character is in the chapter and what perspective they are in.
A better option would be to have them both be in 1st or 3rd. Or, you could only have one perspective.
Good luck with your writing!