Eu vorbesc puțin română și puțin engleză.

In Romanian the verb ending usually tells you who the subject is, so Eu is optional.
• Vorbesc puțin română… already means “I speak a little Romanian….”
• You include Eu only for emphasis or to avoid ambiguity (e.g. contrasting with someone else).

a vorbi is a regular “-i” verb with these forms:
• eu vorbesc
• tu vorbești
• el/ea vorbește
• noi vorbim
• voi vorbiți
• ei/ele vorbesc

The pronunciation is /vorˈbesk/ (stress on the second syllable).
• -esc = /-esk/
• c at the end is /k/ because it’s not followed by e or i.

Here puțin is an adverb modifying the verb vorbesc (“I speak a little”), not an adjective modifying “română.” Adverbs do not agree in gender or number, so you always use the masculine form puțin.
If you treat it as an adjective you’d say puțină (feminine), but then it would be tied to the noun:
• Am puțină apă. (“I have a little water.”)
With vorbesc, stick to the adverb:
• Vorbesc puțin română.

Yes. One puțin covers both languages:
• Vorbesc puțin română și engleză.
Repeating puțin simply adds emphasis that you speak each language only a little.

Romanian does not capitalize language names or adjectives derived from nationalities. So you write
• română, engleză, spaniolă
all in lowercase (unless they start a sentence).

When you talk about languages as direct objects, you generally use the bare (unmarked) form. They act like uncountable nouns here. You don’t need “o” or any article:
• Vorbesc română.
If you did add an article, you would be specifying “the language” (e.g. limba română).

• Vorbesc română = “I have the ability to speak Romanian.” (language skill)
• Vorbesc în română = “I’m speaking in Romanian [right now].” (language used in conversation)

The normal order is:
verb → adverb → object
e.g. Vorbesc (verb) puțin (adverb) română (object).
Moving the adverb after the object (Vorbesc română puțin) sounds awkward and is not standard.

Yes, colloquially you can use un pic or diminutives like puțintel:
• Vorbesc un pic de română și un pic de engleză.
• Vorbeam puțintel română.
Note that with un pic you often insert de before the noun (un pic de română), though dropping de is also heard in speech.