Una regla importante en casa es no usar el celular en la cena.

In Spanish, every noun has a gender. Regla is a feminine noun, so it must use the feminine article una, not un.

• una regla = an important rule
• un problema = a problem (masculine)

The adjective importante doesn’t change because it has the same form for masculine and feminine in the singular.

Both are grammatically correct, but they don’t feel exactly the same.

• en casa usually means at home in a general, emotional, or habitual sense:
  
  • Una regla importante en casa = An important rule at home (in our household).
• en la casa is more concrete and physical: in the house / in the building.

So en casa here talks about your home environment and family habits, not necessarily the physical structure.

In Spanish, the infinitive (like usar) can act as a noun, similar to “to use / using” in English. So:

• no usar el celular en la cena = not using / not to use the cellphone at dinner
• The whole phrase is the “thing” that es (is):
  
  • Una regla importante … es no usar el celular…

You could rephrase with a clause:

• Una regla importante en casa es que no usamos el celular en la cena.
  But the original with the infinitive is shorter and more neutral, and it sounds very natural in rules.

Yes. You can switch the order without changing the basic meaning:

• No usar el celular en la cena es una regla importante en casa.

Spanish allows some flexibility in word order. Starting with No usar el celular en la cena… puts more emphasis on the action (not using the phone) rather than on the idea of “a rule.”

Spanish normally uses a definite article with singular countable nouns in general statements:

• No usar el celular en la cena. = Don’t use the cellphone at dinner (cellphones in general).

You can drop the article in some very informal signs or notes, especially in lists:

• Prohibido usar celular.
  But in a full sentence like this, el celular is the most natural and standard form.

Regionally:

• celular or teléfono celular = Latin America
• móvil or teléfono móvil = Spain

Teléfono alone can mean “phone” in general (landline or mobile), but today context usually makes it clear. In Latin America, for everyday speech, celular is the safest and most natural choice for “cellphone.”

Both are possible:

• en la cena = literally at dinner / in the dinner
• durante la cena = during dinner

En la cena is a little more general and very common in rules about meals. Durante la cena emphasizes the time period more strongly. You could say:

• Una regla importante en casa es no usar el celular durante la cena.

This is still correct; it just slightly shifts the focus to the time span.

No, that would be wrong in standard Spanish.

With cena (dinner), you normally need the article when you specify a situation like this:

• en la cena = at dinner
• para la cena = for dinner

There are some fixed expressions without an article (like después de cenar = after dining), but en cena by itself is not used.

Yes, and that’s also very natural.

• Es importante no usar el celular en la cena. = It is important not to use the cellphone at dinner.
• Una regla importante en casa es no usar el celular en la cena. = An important rule at home is not to use the cellphone at dinner.

The first focuses on importance in general. The second presents it specifically as one of the household rules.

Yes, that’s correct and very common. The meanings are very close:

• Es importante no usar el celular en la cena.
  
  • Infinitive; more impersonal, like a general principle or rule.
• Es importante que no usemos el celular en la cena.
  
  • Subjunctive; emphasizes what we (or some group) should do.

The version with que + subjunctive highlights the people involved a bit more.

Common options in Spanish for a rule or sign are:

• No usar el celular en la cena.
• No se permite usar el celular en la cena. = Using the cellphone at dinner is not allowed.
• Prohibido usar el celular en la cena. = Using the cellphone at dinner is forbidden.

Using the bare infinitive (usar) like this is a standard way to write impersonal rules and instructions.