Financially, we haveMORE NATURALLY: We have managed to saved some money.

In terms of health, weMORE NATURALLY: Moreover, my family has haved no major illnesses.

Before, heMy husband used to be a workaholic who neverith no had time for me, and we were on the verge of divorce, but now, h. However, my husband's attitude seems to have changed his mind to band his become closer to me.

ProbablyMany people, as wethey get older, we are losingloose confidence in living alone.

We should continue to cooperate with each other to enjoy a fulfilling life in retirement.

So far, our lifvestyle is has been working well.

I wish it would continue the sahope no major changes come.

What should we do if any of us were to become seriously ill?

WeMy husband and I need to calm down and think carefully.

Looking back on this year, it has been a good year for our family overall.

You can remove "on this year", since you mention the year later on in the sentence.

Financially, we have saved some money.

A more natural way to say this:
"Financially, we were able to save up some money."

In terms of health, we haved no major illnesses.

It's better to use the past tense "had" here since you're looking back on the year and talking about time that has already passed.

Three of our five cats are also elderly, but in good health.

I'm glad to hear that!

Speaking of leisure, we have nevern't traveled to any tourist spots in recent years, because we cannot leave our cats at home.

Probably, as we get older, we are losinge confidence in livingour capability to live alone.¶
¶
or: Probably, as we were getting older, we were losing confidence in our capability to live alone.

Remember to match the tenses of "get" and "lose".

We basically live apart on weekends, because we want to spend our ownindividual free time how we like.

He stays at a flat nearby or a hotel in Tokyo and returns home on Monday evening when, during which we will have plenty to talk about.

I wish it would continue the sameas it is.

What shwould we do if any of us were to become seriously ill?

Looking backReflecting on thise year, it has been aoverall been quite good year for our family overall.

Using the word "year" twice in the sentence like this feels a bit "clunky".

Rather than use the word "overall", you could use the phrase "on the whole" which sounds a bit more natural in this context.

→ "Looking back, this year has been a good one for our family"

→ "Looking back, this year has been pretty good for our family on the whole."

Financially, we have been able to saved some money.

Your original sentence was perfect grammar. But we often say "been able to save" rather than "saved".

Speaking of leisure, we have neverWe haven't been able to traveled to any tourist spots in recent years, because we canno't leave our cats at home alone.

"Speaking of X" is used when you want to add something additional to what you have already said about X.

However, you haven't mentioned anything about "leisure" yet, so using "speaking of leisure" doesn't make sense.

Before, he used to be a workaholic who never had time for me, and we were on the verge of divorce, but now, he seems to have changed his mind to bhas changed his behaviour and has become closer to me.

Probably, aAs we get older, we are probably losing confidence in livingour ability to live alone.

We should continue to cooperate with each other towork on our relationship and enjoy a fulfilling life in retirement.

We basically live apart on weekends, because we want to spend our own free time how we likeon our own interests.

From Friday morning until Monday evening, we cantypically spend it however we like.

He will stays at a flat nearby, or a hotel in Tokyo, and returns home on a Monday evening when we will have plenty to talk about.

Or, you can adjust the grammar slightly like this:

"He often stays at a flat nearby, or a hotel in Tokyo, and returns home on Monday evenings when we will have plenty to talk about"

I wish it would continue the samefor everything to continue as it currently is.

That’s my missionduty/responsibility.