Most of the issues you mention are in no way simple Democrat vs Republican issues - otherwise things certainly would have changed a lot more under previous Republican administrations and/or congressional majorities. It's just that, like in any two-party system, the parties each represent a wide range of interests and political views, and their moderate wings are probably closer to each other than they are to the more radical wing of their own party.
To take a few obvious examples:
- entitlements: certainly not all Republicans support reforming them - the way Trump, who, possibly correctly, argued that Americans just wouldn't accept serious cuts to entitlements, trounced someone like Christie who made a point of stressing the need for reform, should tell you enough
- immigration: both parties have generally welcomed legal immigration and allowed the numbers to increase; illegal immigration is more divisive, but still there are plenty of Republicans whose positions are indistinguishable from those of moderate Democrats
- spending: has grown under Republican presidents / Congressional majorities as well as Democratic ones, with the two parties having somewhat different priorities, but also aligning on plenty of things
- Olympia Snowe may be a centrist who could easily be a Democrat in another state, but John McCain certainly isn't; despite his reputation as a maverick and willingness to challenge his party, which are anyway less obvious in recent years, any analysis of his voting record still shows he's plenty conservative
- re: "when did a right-wing agenda on the scale of Obamacare get run through against adamant Democratic opposition?": That's one way of looking at it. From the perspective of the liberal wing of the Democratic party - your counterparts on the left - the same fact illustrates the opposite point: that a number of Democrats in Congress are so conservative that they support the right-wing agenda, e.g. on the notorious Bush tax cuts, which indeed makes it unusual for Republicans to push anything important through without at least a few Democratic votes, while the Obamacare vote also saw some Dems voting no, at least in the House.
I'll grant you the SC point, but as I'm sure you're well aware, the Court is rather more complex than just conservatives vs liberals on the majority of cases, just not usually on the highest-profile ones. To take just one example, in the SC opinion that confirmed the legalization of gay marriage in California, Scalia actually sided with the 'liberal' majority, while Sotomayor joined Alito, Thomas and Kennedy in opposition.
Sure, Trump or Cruz can try to pass what they like. And if it's reasonable enough to get near-unanimous Republican approval, they should be able to find a few Democratic votes in the House as well. It's worth pointing out that none of the SC appointees in recent years have been appointed - or rejected - along a straight party line vote. Including Bork, whose rejection may not have been the best ever decision, but one shared by several Republicans, and you can't say he didn't get a fair hearing. This whole current controversy has politicians on both sides manifestly contradicting their earlier positions, hypocrisy all around, but for all the historical parallels made, I've yet to see a single case where the Senate refused to even consider a proposed nominee for ten months, or for that matter where the president failed/declined to propose anyone for that long.