I don't think the word would be inherently interpreted with sexual connotations, but as is often the case, context is all important.
For example, your sentence is lacking context and begins with "Have you heard...?" which suggests some element of gossip. However, if you added context to that, such as:
Do you know who Jim and Tina are playing golf with?
Yeah, they've made a foursome with Jim and Tina.
The issue with your question is that, in isolation, the lack of context seems deliberate - as there's no indication for what purpose they've formed a foursome - and that's where the potential for innuendo appears.
Of course, people will also take cues from your tone and body language, so your meaning should be conveyed correctly, given that you provide sufficient context.
Just to make clear, I'm a British English speaker (and live in that region), but I think it's important to provide a global view. I'm not personally sure that the Americans would see matters any differently, but I do find issues of this nature fascinating.
Any of those sentences could be used and seem completely natural in different contexts. You choose each among those expressions based on what you want to communicate.
Are you talking about one chair or many chairs? That (obviously) determines whether you choose the plural or not. If I asked about multiple spoons, but you answered me with a singular response, it would seem odd. For example, if I said "Would you get me two spoons from the drawer please?" and you responded "There's no spoon here." If I ask about a singular and you responded with a plural it wouldn't be as odd. If I say "Go tell Joe he has a phone call." you could say "There are no Joes in this room - I don't know who you're talking about." even though it's more likely you would say "Joe isn't here."
Are you talking about one specific chair or just any chair? That determines whether you say "there is no chair" or "there isn't a chair". This can be tricky because it really depends on what is in your mind when you say it, and not necessarily anything that has been said earlier. I could say "When you get there, sit in the chair." and if there are only couches when you get there, you might tell me "There is no chair here." (the specific chair that you were going to sit in isn't there) or "There aren't any chairs here" (you looked for any chair to sit in and there were none available).
In the movie the Matrix, there is a scene where a boy is bending a spoon with his mind and he says that to do that first you must realize there is no spoon. He is speaking about a specific spoon. If I asked you to get me a spoon from a drawer that had no spoons in it, you could say "there isn't a spoon in here (for me to give you)." or "There aren't any spoons in here, just forks." or "There's no spoon in here (the specific spoon you want isn't here)." All of those statements are fine and sound natural.
Best Answer
As a general rule, we use 'this' for something immediately in front of us or brought to our attention, and 'that' for something that we are highlighting from a distance.
Example: Imagine you're in a crowded room. If a friend introduced you to someone - brought them to you - they might say "this is John". But, if your friend pointed at someone on the other side of the room, they might say "that is John".
The same is true of 'these' and 'those'. Generally, 'these' is for things brought to you, 'those' are things that are highlighted to you.
Example: If your friend handed you some photographs, he might say "these are photos of my family". But, if he pointed at some photos hanging on the wall, he might say "those are photos of my family".
There are exceptions. For example, if a group of people were in the distance but were intentionally heading towards you, one might ask "who are these people?". Likewise, someone might preemptively say "look at this" before bringing something to you. So, it isn't so much the distance between you and the thing being referred to, but whether it will remain remote.