I don't get this idea that conquest will cost anyone money necessarily, it's clear that Venice is going to decline if it stays territorially small and I think the Venetians can realize this long term trend, this would be enough to push towards more expansion in the mainland.
It really depends on when. From the crusades onward, what was most important to Venice was the immediate hinterland for water and food, in addition trade access to Germanies via the alpine routes. during Venice's silver age of 15th-17th; when the Venetian economy was shifting from international trade towards regional trade with a large emphasis on manufacturing then it was very profitable. By the 18 it was too late.
You need to find a way that conquering Italy would be worth setting aside their commercial pursuits for however many years. They made more money from trade than owning the entirety of Italy would have netted them. Constant rebellions, invasion from north, south, east, and west, and lack of manpower would have tended this conquest towards collapse.
IOTL, the Patricians stratified in wealth post 15th century and the salaries paid to them was suddenly important. Rich patricians paid to be free of posts while the poor patricians took on offices and tried to create new offices (through conquest). Regardless of economics, it was economically advantageous for the numerous poor Patricians to support conquest and they had the political power if nothing else.
Whether Venice can do it is answerable -- i believe they can use their trade connections and expert diplomacy to play their enemies against one another while they're busy expanding the Stato di Terraferma. If they can conquer Milan, then they already got a significant boost to their odds.
The only problem is, i'm afraid, if Venice wants to do it. Founding an empire takes precious time and money, something the Venetian merchant class might not be willing to stomach. There's also the issue of Venice's politics -- conquering vast swathes of Italy would require the Venetian senate to integrate their new citizens (including the hated Genoese) in some way that's satisfactory to both parties, which is easier said than done. Not to mention nearby powers such as France, Austria, Spain, the Ottomans, maybe even the Swiss, who will likely object to an unified Italy.
Another matter of timing; the Venetian Patricians tends to open up their ranks during crisis. Of course they need something systematic; so the disenfranchisement acts of the 13th century (ie Great Serrata which limited new Patrician blood needs to be reversed. Doable, they just need to be convinced of the need. That or do it before the 13th century.
Not that it would be impossible, though. Venice was occasionally willing to engage in campaigns of conquest across northern Italy to eliminate potential threats, until they were exhausted by the defeats of the Italian Wars. One could tamper around with PoD's around that date (such as reversing the defeat at Agnadello) to get the desired result. Keeping the eastern Mediterranean divided between Turkey and Mamluk Egypt could also help in keeping Venice's maritime flank safe for the most part.
IOTL in 1402 the Venetians refused to ferry Timur's host of 100,000+ from Asia minor to finish off the Ottomans; they could simply accept and deal with the chaos as Timur's empire disintegrates after his death as it was held together by his personality. It would be easier to deal with the chaos than the Ottomans next door. Also compared to the Ottomans the Mamluks had severe internal problems with Mamluk infighting, resistance to change, Mamluks extortion, abuse, and terrorizing of the subjects.
The 14th-15th century was the best time, the Hapsburgs were divided between three lines, France occupied in the 100 years war, the Byzantines in terminal decline, the Ottomans are about to be crushed by Timur in 1402, and the Papacy occupied by the Schisms.
As well as manpower; hiring condottiere can only get you so far if you want to conquer all of Italy. There's a (possibly apocryphal) story about condottieri avoiding winning battles for Venice, because if she got too powerful, they'd be out of work again.
It depends, Venice has killed its own share of mercenary captains like Carmagnola suspected of treason. The main difference between Venice and the other city-states was that it wasn't a cash-strapped and unstable signora/oligarchy trying to wage war balanced on stilts. Political transitions tend to be smoother in Venice, it had deep pockets and even bigger lines of credit.
Genoa was even more naval-focused than Venice, with barely any settlement in Italy outside the city proper. Again, Venice's problem was not a lack of money, but a lack of manpower, and no necessity for more land.
Not quite, Genoese Patricians were a mix of shipping magnates and wealthy feudal landowners. The government operated like a publically traded company where you can buy political power, the problem was that it was extremely dynamic, vigorous, and unstable. IOTL when it seemed that the Venetians were about to be destroyed during the War of Chioggia the Venetians united and dug in their heels; when the Genoese were defeated in turn the feudal landowners saw their rivals in Genoa weakened and launched a coup, this would be followed by 7 other coups within a decade. Genoa was fragile and powerful.
Putting aside that there's no reason for age-old rivals Genoa and Venice to consider an alliance, it would only be a combination of enormous wealth.
Agreed, better and more profitable for one to crush the other decisively.
The reason Italy wasn't unified in OTL until the rise of nationalism is that the city-states had a well-developed early concept of "balance of power," and there was a strong interest from both the states within Italy and the major powers outside to maintain that balance of power. Every war in Italy during Venice's golden age was full of constantly shifting alliances, to consciously prevent any one ruler from gaining too much control. When Venice was slightly too powerful for the Pope's liking, it suffered simultaneous declarations from the Pope, the King of France, the King of Spain, and the Holy Roman Emperor (the League of Cambrai). It's just hard to imagine any state uniting Italy during the Middle Ages or Renaissance.
Its not set in stone, IOTL around the end of the 15th century when "The Great Snake" Gian Galeazzo Visconti of Milan was conquering the Po Valley all the literature from the mainland showed an atmosphere of resigned fatalism as it was generally believed that they would lose to Milan eventually. Had Gian not died accidentally in his 50s, he would've had a decent chance at it. All it takes is a generation of relatively okay occupation for the next generation to see Venetian rule as "how it always was".
You might have the best navy in Italy, but Florence et al had better armies with more men.
By the same logic the Venetian Republic should've never had won against Da Carraras, Visconti, Ferrara, and all the mainland city-states it absorbed. By the 15th century Venice was more populated than Florence.