The difference in connotation is that we usually use suppose to make an assumption and let to make a declaration.
Suppose X is true. It follows that Y is false.
We let Z be an integer so that 2Z+1 is odd.
OK. A "stitch" is a single loop of thread, used to bind pieces of fabric (or other material) together, as when one uses a needle to draw a thread through the fabric layers. "Stitch" is countable (though different people may have different ways to count what is a stitch, especially for more complex ones, like an overlock stitch).
"Stitching", then is making repeated stitches, whether to bind up a wound or to put together a garment. (Or make a quilt, etc.)
"Sewing" is the activity involved in making items out of fabric or similar materials, using techniques resembling stitching. (What a "technique resembling stitching" means is subject to individual interpretation, but might include gluing, fastening together with rivets, fusing with heat, etc.) "Sew" is a verb (where "stitch" is both a noun and a verb), though "sewing" can be used as an uncountable noun.
Sewn items might be articles of clothing, curtains, coverings for pieces of furniture, bedding, the "convertible" roof of a car, or a dozen other things.
Either term may be used in a metaphorical sense -- "stitch together an alliance", "sew up a business deal".
Best Answer
As a general rule, use the preposition including when you need a preposition that means (according to wiktionary) “Such as, among which; introducing one or more parts of the group or topic just mentioned. [Eg] ...fill in the details, including your name and address...”.(See Edit 1, below.)Also as a general rule, use the verb include when you need a verb that means (again according to wiktionary) “To contain, as parts of a whole. [Eg] The vacation package includes car rental” or a verb that means “To bring into a group, class, set, or total as a (new) part or member.” Examples of that last usage with the simple present and with the present participle include
Regarding the examples in the question, the following forms are correct. (The “is including” forms are clumsy and unlikely to be used by native speakers, but are not incorrect.)
Edit 1: As Barrie noted, including is not a preposition. Typically it serves as a present participle. See the following extract from OED1 (1901) for some examples of use.