Is there an area to have a picnic with some sandwiches and fruits ( no cooking) ?

I recall seeing signs no food or beverages in the park or in the gardens

I'm not sure. Best to call or check website.

There's seating areas along the way and there's also a table somewhere in the garden with an umbrella and seats so I'd say yes

There are places you could sit and eat but they also prefer you buy food from them. $$$

There are picnic tables near the restrooms by the conservatoryand other places to picnic along the river path immediately next to the Japanese gardens