Такой план невозможен без поддержки команды.

In the present tense, Russian usually leaves out the verb to be.

So:

• Такой план невозможен literally looks like Such plan impossible
• but it means Such a plan is impossible

This is completely normal Russian. If you wanted past or future, then a form of быть would appear:

• Такой план был невозможен = Such a plan was impossible
• Такой план будет невозможен = Such a plan will be impossible

Такой here means such, this kind of, or a plan like that.

So такой план can mean:

• such a plan
• a plan like that
• this kind of plan

It does not usually mean simply that plan in the sense of pointing to one specific plan. For that, Russian would more likely use этот план.

So:

• такой план = such a plan / a plan of this kind
• этот план = this plan

Because такой must agree with план.

План is:

• masculine
• singular
• nominative case

So такой also has to be masculine singular nominative.

Compare:

• такой план = such a plan
• такая идея = such an idea
• такое решение = such a decision
• такие планы = such plans

This is standard adjective agreement in Russian.

Невозможен is the short form of the adjective невозможный.

Russian often uses the short form when the adjective is the main predicate of the sentence, especially in sentences like:

• План невозможен = The plan is impossible
• Это необходимо = This is necessary
• Задача трудна = The task is difficult

So in this sentence, невозможен means is impossible.

The full form невозможный is usually used more like a regular descriptive adjective before a noun, for example:

• невозможный план = an impossible plan

Very roughly:

• невозможный план = an impossible plan
• план невозможен = the plan is impossible

Yes. The short-form adjective agrees with the noun.

Since план is masculine singular, we get невозможен.

Other forms would be:

• идея невозможна = the idea is impossible
• решение невозможно = the decision is impossible
• планы невозможны = the plans are impossible

So the ending changes depending on gender and number.

Because the preposition без always takes the genitive case.

So after без you need the genitive form of the noun:

• поддержка = support
• без поддержки = without support

This is a very common pattern:

• без воды = without water
• без помощи = without help
• без команды = without a team

Here, though, the phrase is a little longer: без поддержки команды = without the support of the team.

Because поддержка is followed by the person or group giving that support, and that is commonly expressed with the genitive in Russian.

So:

• поддержка команды = the team’s support / support of the team

In the full phrase:

• без поддержки команды

there are really two genitive relationships happening:

1. без requires genitive, so поддержка becomes поддержки
2. поддержка is followed by команды to mean support of the team

So the structure is:

• без
  • поддержки
• поддержки
  • команды

Yes, that is a very natural way to understand it.

Russian often uses the genitive where English might use:

• of
• or a possessive ’s

So:

• поддержка команды = support of the team
• natural English: the team’s support

Both are correct ways to understand it.

Russian has no articles.

So words like a, an, and the are not translated directly. Whether something is definite or indefinite is understood from context.

That is why:

• план can mean a plan or the plan
• команды can mean of a team or of the team

In this sentence, the meaning shown by context will tell you which English article sounds best.

Yes. Russian word order is flexible, and changing it mainly changes emphasis, not the basic meaning.

The given sentence:

• Такой план невозможен без поддержки команды.

is a neutral, natural order.

You could also say:

• Без поддержки команды такой план невозможен.

This puts more emphasis on without the team’s support.

So both mean essentially the same thing, but the focus shifts.

Yes, but it means something slightly different.

• Такой план = such a plan / a plan like this / this kind of plan
• Этот план = this specific plan

So:

• Такой plan невозможен... talks about a type or kind of plan
• Этот план невозможен... talks about one particular plan

Both are correct, but they are not interchangeable in every context.

It is quite neutral and natural. It would work well in:

• business discussion
• project planning
• team management
• formal or semi-formal writing

Nothing in it is slangy or especially literary. It sounds like normal standard Russian.

A word-by-word breakdown is:

• Такой = such / this kind of
• план = plan
• невозможен = impossible / is impossible
• без = without
• поддержки = support, in the genitive
• команды = of the team

So the structure is:

Such a plan is impossible without the team’s support.