FB is sending friend requests without me knowing. I'm getting messages that somebody accepted my friend request I did't send.

kind of - what I notice is that if one of your friends has a 1000 friends then facebook will send a "you might know this person do you want to send a friend request to them " which means you get a friend request from someone you may not know. But the unknown person may be via a mutual friend. My facebook has a friend who has 1000 friends so I could potentially get 1000 friend requests and 1000 postings being shared on my timeline .
not sure if it also does this randomly

Also anyone can search facebook and request to be a friend to someone they do not know !.

very smart to select only friends that you know and trust
any person who demands that you include them in your list of friends may have an ulterior motive because once they are friends , their friends can read your posts and can become obnoxious to you
it is like a back door into your privacy

You are sending out Friend Request to people that you "DO NOT KNOW". Soliciting Friends (Look at your FEMALE to MALE Ratio). If you are sending to just Females you do not know then you are being considered a "STALKER" and if enough people complain then there is your answer.

Asking to be Friends with someone on Social Media to people you do not know may be your issue. Why not try becoming friends with people you know and building up friendships?

Try sending a message. If that wont work post to the wall that she needs to unblock you. If she unblocks you, you can accept the request.

Btw, I’m available to help over the phone in case u need at https://www.6ya.com/expert/robert_33deecd2f8e91168

This comes from the FB help desk -
If you've been blocked from sending messages on Facebook, it may be because you sent a lot of messages recently or people reported your messages as unwelcome. Make sure to use your real name and picture to help the people you're messaging recognize you.
Please also keep in mind that this block is temporary. You can still use other Facebook features to connect with your confirmed friends while you're in this block.
Once your block is over, please only send messages and friend requests to people you know personally. To learn more about our policies, please review the Facebook Community Standards.
Note: If you're blocked from sending messages, you may also be temporarily blocked from sending friend requests.

This comes from Facebook help desk:
If you've been blocked from sending messages on Facebook, it may be because you sent a lot of messages recently or people reported your messages as unwelcome. Make sure to use your real name and picture to help the people you're messaging recognize you.
Please also keep in mind that this block is temporary. You can still use other Facebook features to connect with your confirmed friends while you're in this block.
Once your block is over, please only send messages and friend requests to people you know personally. To learn more about our policies, please review the Facebook Community Standards.
Note: If you're blocked from sending messages, you may also be temporarily blocked from sending friend requests.

Dear User,This is not laptop issue,This is the issue with your facebook account.You might have posted any views or pictures or post which violates the FB terms.So revisit your FB account and send mail to FB helpdesk.

u had given any warning from facebook before sending request.
just wait for an one week then try to send request.
send request only who knows you. otherwise fb block your request sending.
if nothing after one week then u can send complain through feedback sheet.

Actually your question didn't gave me a good picture on what is the exact problem.
Did you mean you can't send friend-requests anymore?

Well, this is not a critical problem. Some people on facebook simply send hundreds of friend requests to girls and boys - facebook is not actually a dating site - so Facebook needs to stop that.

As a quick solution, ask some of your real friends to send friend requests TO YOU.
when you get more requests from others, you could send out! Plus, people whom you send requests must accept them in order to permit you to send more requests.

I'm guessing the difference between you and "them" is that you happened to friend someone or a few people that don't like to get friends that they don't know in facebook and reported you as a abuser.

I suppose you got unlucky and someone or a few people didn't like you friending them. Facebook alone won't throw you out, it means that someone complained.