When I tried to Install the patches I got this error.

JFolder::create: Infinite loop detected
Unable to create destination
Error installing file "administrator/defines.php"

My tmp folder was outside the root and my log folder also.

I moved both tmp folder and log within my root path and modified my settings on configuration.php

I kept on having the same issue. I played with my php.in open_base_dir allowing those new folders specifically but the error was still present. I disabled php.ini completely and then I could workaround this problem.

I enabled php.ini again to pass over the subsequent Server error and it did the trick.

Which php.ini command could be causing that Infinite loop problem?

Once the patches are installed will I have some issues related to it?

Let's see.

The "Infinite Loop detected" is a message generated by Joomla when it loop in the creation of a folder.
When a "complex" directory need to be created, (ie. dir1/dir2/dir3), theorically, there are 3 directories to create. It may happen that when you have a permission issue, Joomla can not create the dir1 and in this case retry several time to exceed the limit of 10 (or 20) I don't remember.

If you want to temporarly bypass the potential permission issue, try using the joomla FTP layer. In this case, you will use the FTP login for the permission of the files and folder. This should allow creating the folder.

When open_basedir is active on a website, this let me suppose that the owner of the files and folder is "apache" (or nobody) or something like that. In this case, it is possible that it does not has the permission to access or write into your directory. Without the FTP Layer, it may perhaps required to put a chmod 777 in the directory where you want to write.