Friendship is based on the premise of mutual respect, not allow a bit enforcement, interference nor controlment.

这个句子是很典型的中式英语，有缺陷甚至错误。分析如下：

the premise：意为“前提”。其实它跟 be based on 连用，纯属多余，直接删除。包括 of 也删掉。即：

Friendship is based on mutual respect.

其次，not allow... 为错误表达。改为现在分词 not allowing... 作伴随或方式状语。或者使用并列句。

Friendship is based on  mutual respect, not allowing .....

Friendship is based on  mutual respect, and does not allow .....

最后，a bit 不能直接作定语，需要加of,   即： a bit of。nor 改为 or。

句子改为：

1. Friendship is based on mutual respect, not allowing a bit of enforcement, interference or controlment.

2. Friendship is based on mutual respect, and does not allow a bit of enforcement, interference or controlment.