Я люблю весну.

No, you don’t have to include Я. Russian is a “pro-drop” language, which means the verb ending often tells you the subject.
• Люблю already indicates “I love.”
• Omitting Я is perfectly natural in casual speech or writing: Люблю весну.
• Including Я adds a bit of emphasis or clarity.

Люблю is:
• 1st person singular (“I”)
• present tense
• imperfective aspect (indicating a general or ongoing feeling)
The infinitive form is любить (“to love”).

Because весна (“spring”) is the direct object of the verb люблю, so it takes the accusative case. Feminine nouns ending in -а switch to -у in the accusative singular: • Nominative (subject): весна
• Accusative (direct object): весну

In Russian, most nouns ending in -а or -я are feminine. A quick check:
• весна, мама, нога are feminine.
• You can also verify gender in a dictionary if in doubt.

Pronunciation (approximate):
• Я = “ya”
• люблю = “lyub-LYU” (stress on the second syllable)
• весну = “vyes-NOO” (stress on the second syllable)
IPA transcription: /ja lʲʊˈblʲu vʲɪsˈnu/.

• Я люблю весну literally “I love spring” – a strong feeling.
• Мне нравится весна literally “Spring is pleasing to me” – closer to “I like spring.”
Notice with нравиться you use the dative case for the person (мне), and the noun stays in nominative (весна).

No. Seasons are common nouns in Russian, so they are written in lowercase, unless they start a sentence: • правильно: я люблю весну
• неправильно: я люблю Весну

You just replace весну with the other season in the correct case:
• Я люблю лето. (“лето” is neuter; accusative = nominative)
• Я люблю осень. (“осень” is feminine ending in -ь; accusative = nominative)
• Я люблю зиму. (“зима” is feminine; accusative зиму)