The phrase "and eventually opening a" is correct and usable in written English.
It can be used when discussing a process or sequence of events that leads to the act of opening something, such as a business or an event.
Example: "After years of planning and hard work, she is excited about the possibility of and eventually opening a new café in her neighborhood."
Alternatives: "and ultimately launching a" or "and finally starting a".
He hopes to train in electronics and eventually open a shop.
In 1996, U.C.B., as it's known, moved to New York, started a training program, and eventually opened a theatre.
In 1999, he closed the theater in Union and eventually opened a house in Bloomfield, using the same name.
His father, a tenant farmer, played accordion; his mother did farm work, ran informal horse races called bush tracks and eventually opened a dance hall.
He later worked in his uncle's gun business building revolvers, sold guns wholesale to law enforcement, and eventually opened a retail shop.
Drifting to the open city of 1960s San Francisco, he developed an interest in art and design and eventually opened a series of stores there specializing in midcentury modern furniture and appliances.
Faced with a noncompete clause, he traveled for a bit and eventually opened a bakery called Cox Cookies and Cake on the naughty side of Soho in London, selling baked goods that cheekily made references to the peep shows and X-rated video stores that flanked his storefront.
But over the years, this self-described "nice Jewish girl" grew to love her adopted neighborhood, where she cycled through 17 roommates and was free to make art and, eventually, open a gallery that she still operates in her living room.
The key, for more than 200km, was using Chris Froome and Steve Cummings to ride at the front of the peloton, keeping the tempo high but ignoring the temptation to chase breaks by the seven men who went off early and eventually opened a gap of eight minutes, or by the half-dozen who followed them up the road with 150km to go.
After his discharge he studied various martial arts, devised his own fighting style based on his war experience and eventually opened a Kung Fu karate studio in San Diego in the mid-1980s.
