Learn Icelandic: Ég stend úti.

The dictionary form (infinitive) of the verb is standa. Because it is a strong verb, its main vowel changes in the singular forms of the present tense (I, you, he/she/it). Here, the a changes to an e for the "I" form, giving us stend.

Will the vowel stay as an e if I want to say "we stand"?

No, it changes back. In the present tense, strong verbs only have this vowel change in the singular. If you say "we stand" (við stöndum) or "they stand" (þau standa), the e disappears.

Why doesn't stend have a vowel at the end, like ég tala does?

Unlike regular (weak) verbs that usually end in a vowel for the "I" form, strong verbs like standa do not take an ending for ég. You are left with just the changed stem: stend.

I have seen the word for outside spelled as út. Why is it úti in this sentence?

Icelandic has two different words for "outside" depending on movement. You use úti when you are in a stationary position or already located outside, such as when you are standing. You use út when there is active movement towards the outside, like when you are walking out the door.