Learn German: Ich lache. - I am laughing.

German does not have a separate "am doing" tense like English does. The single present tense form ich lache covers both "I laugh" (a regular habit) and "I am laughing" (happening right now).

Why does the verb end with an -e here?

For regular verbs, the "I" form (first-person singular) always ends in -e. You take the dictionary verb lachen (to laugh), remove the -en ending, and add -e to match ich.

If I added more words to this sentence, would lache stay in the same place?

In a standard German statement, the working verb (like lache) must be in the second position. If you put another word first, the verb still comes second. For example, if you start with heute (today), it becomes Heute lache ich.

Is ich always capitalized like the English word "I"?

No, ich is only capitalized here because it is the first word of the sentence. In the middle of a German sentence, you must write it in lowercase.