Conventions adopted for extended reals

It is known that $0^0$ despite being an indeterminate limit form, is usually defined to be equal to $1$. I wonder whether similar conventions exist for some other "indeterminate forms" in the context of two-point compactifications of real numbers. It would be great if someone showed that some authors used these conventions.

Particularly I am interested to know about usage of the following conventions:

$1^\infty=1$

$0 \cdot \infty=0$

$\infty^0=1$

$\frac 00=0$

I also would be interested whether any author proposed distinguishing between "definable" indeterminate forms (those which can be conveniently defined to have certain value, like $0^0$, $1^\infty$) and those which are more problematic, like $\infty-\infty$ or $\frac\infty\infty$ which cannot be conveniently defined.