Is the Lightning Network used strictly for small transactions between two parties or can one party use it to send a large quantity of BTC (e.g. 35 BTC) to the other party? Is there any advantage to sending large amounts using the Lightning Network vs. using the normal bitcoin Blockchain?
The reason why large payments fail on Lightning is that the likeliness of finding a route that has enough outbound & inbound liquidity on each hop and reaches the destination, gets smaller the larger your amounts are. Of course, Lightning tries to split the payment and use multiple routes, but much larger sums than what you mentioned can already fail.
You can work on your 'connectivity' by opening more and larger channels. Once you're better connected, your routing abilities will improve.