While fundraising, a fund should not have a publicly viewable website in order to avoid any appearance of general solicitation.  The management company can have a website with information on its team members, their past activities (subject to confidentiality obligations) and the types of startups that they are looking to attract.  The management company should not have any reference to any fund that is raising funds.

I guess anyway, a fund does not have a website; it's the website of the management company. I wonder if it's just semantics...

So if I understand correctly, if I'm not mentioning a specific fund or fundraising activity, I can have a website for the 'management company' on my domain, with all the information you mentioned, and also include contact details and a contact form? 

A fund manager must be careful in not using any publicly available website to attract investors.  If the the website is used to attract investors in any manner, this would be considered general solicitation.  The fund manager should avoid directing investors to a website which is used to disseminate information in relation to the fundraising.  The language and context matters.  For example, language that could be interpreted as a presentation of the fund's thesis could be problematic.