Learn Russian: Впереди я вижу большой сад.

Впереди is an adverb of location used when something is already situated in front of you. It answers the question 'where?'. You would use вперёд for motion or direction, answering 'to where?', like when telling someone to walk forward.

Why does видеть (to see) become вижу in this sentence?

This verb has a consonant mutation in the first-person singular form. The д in видеть changes to a ж, making it я вижу. In all other present tense forms, the д remains, such as in ты видишь (you see) and они видят (they see).

Could I use the perfective verb увижу instead of вижу here?

No, because увижу is the future tense meaning 'I will see' or 'I will catch sight of'. Perfective verbs do not have a present tense. Since you are describing an ongoing state of what you are seeing right now, you must use the present tense of the imperfective verb видеть.

Why doesn't the ending of большой сад change if it is the direct object?

Большой сад is indeed in the accusative case, which is used for direct objects. However, сад is a masculine, inanimate noun. In Russian, inanimate masculine nouns and their adjectives in the accusative case look exactly the same as their dictionary form.