"Many videos" doesn't really say a lot about the level of usage you anticipate - it is very easy for such a site (particularly a "Youtube" style site) to overwhelm low cost shared hosting services - a dedicated server may be more appropriate for this use.
Dreamhost [doesn't register .pt domains, but if your registrar allows you to use DreamHost nameservers you should have no problem hosting such a site on DreamHost. Note that, since they cannot register a .pt domain, you would have to use some other Domain that DH can register to avail yourself of the "free domain" that comes with each plan.
All DreamHost plans provide for unlimited "free" subdomain hosting, though the number of users/mailboxes is different from plan to plan. You may re-sell hosting, but you have to manage all that yourself, as DH provides no reseller management tools. You can limit the amount of space by user, not by domain. Note that you will be responsible for complying with all DreamHost Terms of Service and policies even if you re-sell space to others - it is still (your account, and you will be responsible for the actions of any users you host under your account.
DreamHost does not use cpanel, but uses a proprietary custom Control Panel. There is no "demo" , but you can see what it looks like by exploring wiki.dreamHost.com, or signing up for a webId from the main dreamHost.com site.
You can forward email. Yes you have POP/smtp and webmail.
I have no idea what you are asking here. You can host any domain , or subdomain, here if you can properly point DNS to it (see your registrar) You can also host sub-domains here even if the domainis registered somewhere else. You cannot register a .pt domain, but you can register a domain for which DH is a registrar, and it will be free as long as you maintain the hosting plan.
Zend optimizer is supported.