1.when you create a file in a directory, group will get only read permissions.
This could be intended by the admin for your protection. If you want your 'Group' to have read and write access, you can do this:
user@host-$ chmod 775 /folder/filename
doing this your group can Read, Write and Execute the file you allowed them. but this is not advisable either, do it to your own risk.
So you need to do changes so that for that user when ever he creates a file complete group should be having write permissions on that file
You can make a global change by altering the mask. Again this is not safe.
user@host--$ sudo umask 0002
then whatever he creates the group can Read, Write and Execute. Not safe!
2.there are two groups group1 and group2 and user user1's primary group is group1. make changes so that user1 can do any changes in group2.
can someone answer these with explanations
make user1 a member to group2. Use your applet, its so easy.
Next time please specify what distro you are running so that the answers can pinpoint an effective solution for you. Meantime, to hasten up experience with Linux it is good to download here
a tutorial and read from it anything you wanted to know about permissions, groups, users, and important commands.
Hope this helps.