Forced suppression of all cravings including harmless ones

1. Are there any karmic consequences from the harmless consumption of a slice of cheesecake? And why?

It depends on what the karmic intention is. Eating cheesecake can be interpreted as indulgence in pleasure, and is likely to prolong further craving as it's vipaka. As such it will also risk reinforcing the notion of self, maintaining samsara.

2. Should lay people forcibly suppress all their cravings (which includes the craving to eat a slice of cheesecake) or only those that violate the five precepts, Right Speech, Right Action and Right Livelihood? And why?

By definition, lay people are not required to do anything "forcibly", let alone suppress cravings. The suttas merely suggests the layman precepts as a way of life and an entryway into dhamma.

3. Should monks forcibly suppress all their cravings (which includes the craving to eat a slice of cheesecake) or only those that violate the five precepts, Right Speech, Right Action and Right Livelihood? And why?

Arguably, any precept is not intended to be forcibly followed. They are voluntarily made wovs - if anything - as far as i understand. A monk would then follow the additional three or five precepts along with the five initial ones.

4. For questions #2 and/or #3 above, if your answer was "no" to forcibly suppressing all cravings, then I guess entertaining and fulfilling such a craving (to eat a slice of cheesecake) is ok. Is that so?

The way i understand it the purpose of the precepts is not based on permission or prohibition as much as it is offered as a self chosen, volitional effort to end cravings/the notion of a self/samsara.

5 Are there any negative consequences with respect to forced suppression of all cravings (including harmless ones)?

If one emphasises "forced", there is a risk one reproduces new craving in terms of vibhava-tanha (craving elimination) or silabbatupadana (clinging to blind doctrines). Proper knowledge will be a better motivation for further honing skillful karma, not forcing yourself.

1. Yes, there are kammic consequences to any volitional act because as the name implies, it entails volition, or more precisely, it has an intention. In simple terms: If you give into a craving, it's temporarily stilled, but comes back afterwards due to it being reinforcing.

2. Buddhist principles are not commandments. Lay people in this regard are adviced to restrain themselves in the realm of the five precepts, and if they want, they can undertake 8 precepts (which includes celibacy), but this is not mandatory.

If you come up with idealistic ideas of surpressing any desire, you will be full of guilt. The arising of craving of sense objects is determined by the degree of the sensual element. The more you feed it, the more the sensuality element grows. It's only with Vipassana that you can ultimately uproot all "evil" tendencies.

3. With monks it's a bit different. If they're genuinely practise the Buddhist path & experienced some bliss (Samadhi for example), it's easier to let go of cravings. Since monk's goal is Nibbana, it makes sense to overcome all cravings that exist. That's why they renounced the world & material things, to make it at least easier for craving not to arise. Environment is very important, but by no means that means that monks have little craving.

With regards to your last question, it's impossible to surpress all cravings. Once the five hindrances are active there will be craving & attachment. If you haven't experienced the higher happiness of the path, you will inevitably cling to sense pleasures. It's the same as with eating a delicious meal & an ordinary meal.