Она способна справиться.

Because она means she, so the adjective must agree with a feminine subject.

• способен = masculine
• способна = feminine
• способно = neuter
• способны = plural

So:

• Он способен справиться. = He is capable of coping / managing.
• Она способна справиться. = She is capable of coping / managing.

Способна means capable, able, or equal to the task.

In this sentence, it suggests that she has the ability, strength, or competence to do it.

It is a little different from simply saying может (can), because способна often emphasizes:

• ability
• capacity
• fitness for the task
• sometimes confidence in someone’s potential

So Она способна справиться can sound a bit like:

• She is capable of handling it.
• She has what it takes to manage.

Because after способен / способна / способны, Russian commonly uses an infinitive to say what someone is capable of doing.

Structure:

кто-то способен + infinitive

So here:

• Она = she
• способна = is capable
• справиться = to cope, to manage, to handle it successfully

This is similar to English is capable of doing, though Russian uses the infinitive directly.

Справиться usually means to cope, to manage, to handle something successfully.

Very often it appears with с + instrumental:

• справиться с работой = to cope with the work
• справиться с задачей = to handle the task
• справиться с проблемой = to deal with the problem successfully

In Она способна справиться, the thing she is coping with is not stated, but it is understood from context.

English often needs an object like with it, but Russian can leave it out if it is obvious.

This is about verbal aspect.

• справиться = perfective
• справляться = imperfective

Here, справиться focuses on a successful result: she is capable of managing it successfully / getting through it.

If you used справляться, it would sound more like being able to cope in general or repeatedly.

Compare:

• Она способна справиться. = She is capable of handling it / succeeding in dealing with it.
• Она способна справляться с трудностями. = She is capable of coping with difficulties in general.

So in your sentence, the perfective verb is natural because it points to a complete, successful handling of some situation.

Yes. Russian often leaves out the object when it is clear from context.

So Она способна справиться may imply:

• with the task
• with the problem
• with the situation
• on her own

A fuller version could be:

• Она способна справиться с этим. = She is capable of handling this.
• Она способна справиться с задачей. = She is capable of dealing with the task.

Without that extra phrase, the sentence is still perfectly natural if the listener already knows what is being talked about.

Both can mean something like She can manage, but they are not identical.

Она может справиться

• more direct
• often just means she can do it
• may refer to possibility or practical ability

Она способна справиться

• stresses capability or inner ability
• can sound more evaluative
• often suggests confidence in her competence

Very roughly:

• может = can
• способна = is capable of

In many contexts they overlap, but способна sounds a little stronger and more character-based.

It is fairly neutral, but slightly more elevated than everyday может.

• Она может справиться. = very common, everyday
• Она способна справиться. = still normal, but a bit more thoughtful or formal
• Она в состоянии справиться. = also possible, often a bit formal or emphatic

So Она способна справиться would sound natural in conversation, writing, or encouragement, especially when emphasizing someone’s ability.

Yes, Russian word order is flexible.

The most neutral order here is:

Она способна справиться.

But other orders are possible for emphasis, for example:

• Справиться она способна.
  Emphasizes справиться: As for handling it, she is capable.

• Она справиться способна.
  Possible, but less neutral and more marked in style.

For learners, the standard order Она способна справиться is the safest choice.

Yes, but the meaning changes.

• Она способна справиться. = She is capable of dealing with it successfully.
• Она способна справляться. = She is capable of coping / able to cope in general.

The version with справляться sounds more general or habitual, and it often wants an object:

• Она способна справляться с трудностями. = She is capable of coping with difficulties.

So both are grammatical, but they are not interchangeable in every situation.

Very often, yes. способный can be used in a few common patterns.

1. способный + infinitive

   • Она способна помочь. = She is capable of helping.

2. способный к + dative noun

   • Она способна к языкам. = She is good at languages / has an aptitude for languages.

3. As a general adjective meaning talented / capable

   • Он очень способный студент. = He is a very capable student.

So in your sentence, it is the first pattern: способна + infinitive.