Learn Swedish: Ser du tecknet? - Do you see the sign symbol?

The base word for "sign" is ett tecken. It ends in an unstressed -en. For many words ending in unstressed -el, -er, or -en, we drop that extra e before adding the definite ending. So, instead of teckenet, it shrinks down to tecknet.

Where is the word for "do" in this question?

Swedish doesn't use a "do" word to ask questions like English does. Instead, you just swap the verb and the subject. "You see" is du ser, but to ask "do you see?", you just flip it to ser du?

Can I use tecknet to talk about a street sign?

No, ett tecken usually means a symbol, a written character, or a physical gesture. For a street sign or a painted sign on a shop, you would use the word en skylt.

How does the ending of tecknet show its gender?

Tecken is an ett-word (ett tecken). You can tell because its definite form ("the sign") gets a -t ending to become tecknet. If it were an en-word, the definite ending would use an -n.