If I am an 18 year old US citizen and I have been married to my husband for 9 months and 7 days, can I give him papers or apply for his residency?

It depends on how he entered the US. If he entered the US lawfully, you could petition for him the day you married. If he entered the US unlawfully, it does not matter how long you are married because under the current immigration laws, he is not eligible to legalize his status within the US although he may be eligible for temporary work authorization under DACA. Please let me know if you have any additional questions or how I can be of further assistance to you in this matter.

It depends on the circumstances of your husband's situation. But at a minimum, you will need to submit an I-130 relative petition on his behalf to start the process.

Yes. but note that in applying for a green card, there are several considerations that you may need to consider. All of those considerations cannot be addressed in this kind of forum and as such, it is best that you consult with a well recommended immigration attorney.

It depends on what the current status of your husband is and how he originally entered this country. If he came on a visa and overstayed, for example, he can adjust status to a legal permanent resident now, provided that he has no serious criminal history. If he entered illegally, he may be required to return to his home country in order to consular process back into the US, and before he does that, he would need to obtain an unlawful presence waiver for staying in the US illegally. If he is currently in status and is present in the US legally in some legal status, he can adjust status now to a lawful permanent resident.