Your baby is still too young to start talking or displaying her intelligence, but that doesn't mean you cannot teach her things. You'd like her to start reciting ABCD or counting upto 10 as soon as possible, these are probably not what you should focus on right now.
Getting down the bed
Your baby will possibly learn on her own how to get down the bed by herself without rolling over, but with your help she will learn this even faster, and save herself a few more falls.
Initially your baby will be unaware of her surroundings, and will not be able to distinguish between various levels of height. At this time she will just roll or crawl off the bed without a care, and land thud on the floor if you are not careful. But pretty soon you will see her gaining awareness, and she will be hesitant to crawl further than the edge of the bed, and may try to reach down with her hands and gradually inch forward. Until again she lands with a thud! Teach her how to get down by herself, by constantly turning her around until her legs hang off the bed, and then help her get down.
Do this at various intervals through the day, around ten times at a time. Pretty soon she will get the hang of it. And when she does come down by herself, make sure you clap your hands and show how excited you are.
Controlling separation anxiety
Start getting your baby used to having other people around from an early age itself. Babies who go to day care are used to being surrounded by other people, but a new face may still take time for them to get used to. Similarly, have friends over often or go to their homes, fix up play dates and encourage your baby to socialize. Your baby may still enjoy being with you, but once she's used to others, she will not get so anxious.
Another tip to control separation anxiety is to get her used to being alone. You may want to rush to calm her everytime she cries, but if she learns how to self-sooth, she will be happier and less dependent on you.
Don't keep carrying her around all the time. You don't want her to cling to you. Instead, be in the room with her so she can see you, and nip out of the room every now and again. Keep coming back after longer intervals, so she gets used to you being in and out.
Eating out
Go to child friendly restaurants and take your baby with you as often as possible. This will help her learn how to behave in a public place. Initially she may create a scene and you may prefer just leaving her at home, but do take her along. Sit outdoors, where her cries will just get dispersed with the wind, and encourage her to stay seated in one place. Give her a biscuit or something to much, so she stays happy.