Learn Spanish (Latin America): La familia tiene siete perros y ocho pájaros. - The family has seven dogs and eight birds.

Even though a family has many members, la familia is a single grammatical unit (one family). Just like in English where we say "The family has" rather than "The family have", in Spanish we use the singular "he/she/it" form, tiene.

Do numbers like siete and ocho change to match masculine or feminine words?

No, the numbers zero through fifteen (including siete and ocho) stay exactly the same whether the noun is masculine or feminine. If the family had female dogs, it would still be siete perras. The only exception is the number one (uno), which changes to un or una.

Are numbers always placed before the noun they are counting?

Yes, cardinal numbers (numbers used for counting) always go directly before the noun, just like in English. That is why it is siete perros and never perros siete.

Why does the word pájaros have an accent mark over the first "a"?

The written accent tells you to put the stress on that specific syllable when you speak. Without it, standard Spanish rules would make you stress the second-to-last syllable. The accent mark forces the emphasis to the front: PA-ja-ros.