I have menu items like "Logs and Statistics" and I thought we could mention it as "Logs & Statistics".
What is the recommended way?
In my experience, I tend to use ampersands in any title, and the word "and" in sentences and other body content.
So in your case, I would likely use "Logs & Statistics" in the menu. In my opinion, visually it makes the titles look more concise. This has the additional benefit of saving precious real estate in something like a navigation menu as well.
Ultimately, this is a bit of a personal design choice, and there is no "right" answer. However, whatever you do choose, you should be consistent across the application.
I would not recommend to use any "AND" or "&", instead trying to find one level up terminology (Ex: reports) will be better. I would like to ask;
Can you? Sure.
Should you? That comes down branding.
There are multiple opinion pieces out there related to the use of "and" vs. ampersand. The question has been asked over on English.SE before and has a fair number of very good answers: When to use & instead of “and”
Grammatically it is generally seen as less formal. Unless space is a consideration, the word "and" is preferred (from a formal English grammar point of view). Dealing with company names, logos, and other artistic considerations can change the preferred usage as well.
All that comes down to your products brand. "&" if a less formal tone is appropriate, "And" if you prefer a more formal tone - space allowing.
One other concern that may affect your decision is the use of the symbol in other languages. Each language has different usage considerations and someone from (say...) Germany can interpret the '&' symbol in a different way - for better, or worse.